Condensed Matter Physics at the Aspen Center for Physics during the First Fifty Years
by Ravindra N. Bhatt
Phase I. The early years (1962-1979): The Growth of Condensed Matter at the Aspen CenterCondensed Matter Physics, or Solid State Physics as it was then called, had a slow start in early years of the Aspen Center of Physics (ACP). Much of the activity during the first decade involved participation by a few key players who, convinced of the unity of all subfields of physics, decided to participate in activities at the Center, in parallel with their particle physics and (later) astrophysics colleagues. Michael Cohen was one of the founding members of ACP, and a regular attendee during the first decade. The list of solid-state theorists who attended ACP in the sixties is small (12-15 in all), but quite distinguished. A vast majority of them continued their involvement with ACP in later decades as participants on a regular basis. However, two of these - Elihu Abrahams and David Pines - played a central role in convincing key members of the condensed matter community of the desirability of their participation at ACP. Much of the credit for inclusion of solid state/ condensed matter as an important ingredient in this vision of a Center for Physics, where scientists could meet and discuss outstanding problems in all aspects of physics as a unified whole goes to these two. As David Pines recalled, he missed the earliest summers at Aspen because of commitments in Europe, but soon after attending his first summer, he became convinced of the potential importance and impact of the ACP, and he set about persuading other solid state theorists to join him - not only his colleagues at Urbana, John Bardeen, Gordon Baym, and Chris Pethick, but also Elihu Abrahams of Rutgers and Philip Anderson of Bell Laboratories.
The solid state group remained small through the sixties and early seventies, but they discussed many important problems of that era. Anderson, Baym, and Pines each developed interest in problems at the confluence of nuclear-astrophysics and solid state physics, along with colleagues such as Malvin Ruderman. The success of their joint research on pulsar glitches, an astronomical phenomenon, due to superfluidity in neutron stars, using ideas of superconductivity and superfluidity so central to condensed matter, attested to the importance of treating physics as a unified subject.
Examining records from the early seventies, we see a steady rise in the participation by practitioners of the field, who by then felt more comfortable with the name "Condensed Matter Physics". This was a more inclusive title, incorporating within its fold, fields such as quantum fluids, which had become a very active and prominent area of research in the 1960s. Most of the theorists participating at Aspen were pioneers in the popularization of this more inclusive title, and in 1978, the American Physical Society changed the name of the Division of Solid State Physics to the Division of Condensed Matter Physics. However, records of summer activities at ACP several years prior show that Condensed Matter was already very much the operative terminology for the field among participants at Aspen.
By the mid-seventies, Condensed Matter Physics had become a significant part of ACP's activities. Thus, for example, in 1976, the summer program entitled "Current Topics in the Theory of Condensed Matter" attracted a participant list consisting of some of the most eminent members of the condensed matter community. These included, among others, Elihu Abrahams, Phil Anderson, Gordon Baym, M. T. Beal-Monod, Steve Berry, Gerry Brown, Cyrano DeDominicis, Dan Fivel, Gary Grest, Martin Gutzwiller, Bert Halperin, Scott Kirkpatrick, J. Michael Kosterlitz, Jim Krumhansl, Paul Leath, Doug Mills, Philippe Monod, Bruce Patton, David Pines, Mal Ruderman, Wayne Saslow, David Thouless, Gerard Toulouse, and Johannes Zittartz.
The workshop concentrated on three major areas "with substantial unsolved problems", as organizer Elihu Abrahams put it. These were (i) Random systems, (ii) Phase Transitions and (iii) Dynamic Critical Phenomena. With the hindsight of over thirty-five years that we currently have, one could hardly have imagined a more suitable trio. In (i), the next few decades saw enormous strides in the understanding of random magnetic systems - spin glasses, which in turn spawned advances in random networks including biological networks. A second area of unprecedented progress in (i) concerned the problem of localization and interactions in disordered electronic systems. In (ii), not only was there enormous progress in the understanding of thermal phase transitions in the years following the development of renormalization group methods, but starting about a decade and a half later, the subject of quantum phase transitions took off, to a state where it has been one of the leading subjects of enquiry in condensed matter in the twenty-first century. Finally, dynamics, both near critical points, and in the presence of dissipation, was also a very active area of research in the following two decades; its quantum counterpart remains one of the leading areas of investigation to this day.
Of the various offshoots of the three major areas identified in the 1976 condensed matter workshop, the topic of spin glasses was dealt with in some detail at the workshop itself. This was motivated by the seminal advances by Edwards and Anderson and soon after by Thouless, Anderson and Palmer. Having several key players at Aspen that year, including Scott Kirkpatrick, Gerard Toulouse and Cyrano DeDominicis led to a tremendous flowering of these ideas, using the mean-field model by Sherrington and Kirkpatrick (SK) as a backdrop. All of these theorists were active participants at the ACP during that summer and the next. Research on the SK model in the eighties, particularly in Europe, led to profound new understanding of hierarchical structures, replica symmetry breaking, and other concepts that have enriched the field of spin glasses, and led to advances in understanding of random networks as well.
Other topics discussed in the eight formal seminars included the problem of localization in disordered systems; critical phenomena, including the dynamic structure factor near the λ-transition in liquid He-4; and classifications of defects in ordered media using homotopy groups, and its application to superfluid He-3. While two-thirds of the participants in 1976 were new to ACP, the exit report of the organizer stated "another important goal … was to broaden the participation of condensed matter theorists in the Aspen program". This was indeed a prescient remark, for the next year proved very much to be a game changer for condensed matter physics at Aspen.
The year 1977 marked a watershed in the history of ACP, especially for condensed matter. That summer saw the effects of a thaw in Soviet-US relations for theoretical physics. It had become clear that the Soviet efforts in physics were of the highest caliber, and much was to be gained by opening lines of direct communication. As a result of concerted efforts by key US and Soviet physicists dedicated to the idea of scientific cooperation, a large contingent of Soviet physicists, most notably in condensed matter, were given permission to visit the United States, and participate in a special US-USSR workshop, of which David Pines was the principal organizer, at the Aspen Center for Physics. The two teams were led by most eminent scientists, Robert Schrieffer from the US, and Lev Gor'kov on the Soviet end. (It is interesting to note that over the past two decades these two have been colleagues at Florida State University in Tallahassee).
The Soviet team remained in Aspen for a period of eight weeks from July 4th to August 29th. Their members were a truly representative set from the top echelon of Soviet physics, from established leaders to the then emerging young stars, mainly in condensed matter. Besides Gor'kov, the Soviet team was comprised of Igor Fomin, G. Kharadze, I. Kulik, Anatoly Larkin, Sasha Migdal (Jr), Vladimir Mineev, Y. Pokrovskii, Igor Shchegolev, V. Timofeev and Grigorii Volovik. In addition to theorists, they included several leading experimentalists. This induced the US team to invite distinguished experimentalists as well, such as John Reppy and Al Sievers from Cornell, Charlie Slichter from Illinois, John Axe from Brookhaven, B. S. Chandrasekhar from Case Western and Gordon Thomas from Bell Laboratories. For condensed matter, a subject where intense and intimate interaction between theory and experiment was a paramount requirement for significant progress, this was a welcome change in the Aspen culture. Needless to say, the US condensed matter theorists' participant list that year at Aspen, over forty strong, reads like a who's who in condensed matter physics, ranging from preeminent and well-established theorists like Elihu Abrahams, Phil Anderson, Bill Brinkman, Seb Doniach, Walter Kohn, Albert Overhauser, Chris Pethick, David Pines, Phil Platzman, Richard Prange, Maurice Rice, Bob Schrieffer, and John Wilkins, to younger, rising theorists including Ravin Bhatt, Duncan Haldane, Shirley Jackson, H. R. Krishnamurthy and Patrick Lee. Not all the domestic participants during the US-Soviet workshop came from academia; several were from industrial laboratories. Bell Laboratories, in particular, had ten participants, more than any other single institution. The very successful workshop at Aspen induced many Bell labs scientists to become repeat participants at Aspen, both during summer, and later in winter programs. Since the condensed matter community had a large component in industrial and national laboratories in those days, their strong participation in ACP's programs provided a tremendous boost to the rise of condensed matter at the ACP.
Scientifically, the US-USSR workshop focused on several major topics of the period. These included superfluid Helium-3, electron-hole liquids and n-particle complexes in semiconductors, charge density waves, A-15 compounds (the high temperature superconductors of that era), superconducting weak links, as well as multicolor QCD. Most of these fit in very well with the two Condensed Matter Workshops, each scheduled for four weeks, "Strongly Interacting Fermion Systems", and "Charge Density Waves and Associated Phase Transitions". Close to a dozen manuscripts were written by the Soviet scientists during their time at Aspen, a majority in collaboration with US counterparts. In several other cases where there were not collaborative publications, there were intense discussions initiated through informal blackboard presentations in the patio by participants from both sides. Usually, the discussions began at the general level enjoyed by all participants, and then moved onto more technical aspects, leading to the body breaking up into several small groups (e.g. in CDW and A-15s, the participants were Gor'kov, Lee, Rice, Bhatt, Jackson and Overhauser; e-h drops in semiconductors involved Timofeev, Pokrovskii, Thomas, Brinkman, and Rice; and superfluid He-3 involved Mineev, Volovik, Anderson, Fomin, and Pethick). The workshop highlighted the fact that participation by experimentalists was extremely beneficial; their contributions were essential and illuminating for the theorists. From that period on, condensed matter members of the ACP board overwhelmingly supported the idea of having key experimentalists be part of every year's program, an idea that caught on in other fields as well.
The 1977 US-USSR workshop at ACP not only provided scientific collaborations; it also ignited a sense of camaraderie between the scientists from the two very different political systems at a social level. Sharing apartments, cooking jointly, having hikes in the mountains together, sharing food during ACP picnics, all contributed to this sense of being part of a community of physicists endeavoring to unearth new phenomena and insights in a joint partnership across the globe. This workshop gave rise to several subsequent US-USSR meetings. These were held in various locations in the two countries and generated several important international collaborations.
Many of the Soviet physicists were avid hikers, and took to the trails around Aspen as fish take to water. Many were mushroom gatherers, and found the pickings around Aspen bountiful. The first time mushrooms were served at the picnics by the Soviet "chefs," the US counterparts ate them with gusto, unconcerned if this was a plot to undo US science. When all of us returned the next day unharmed and with no gastrointestinal issues, we begged the Russians to repeat the culinary performance at the following picnics as well, and they graciously obliged.
For some of the first time visitors to the western United States, Aspen was enticing, but so was the country for hundreds of miles all around Aspen. When two of us -Shirley Jackson and I -decided to make a 4-day trip to Bryce Canyon, Zion National Park and Grand Canyon, we looked around for people to join us, we needed to look no further than two of my Russian apartment-mates - Mineev and Volovik, who were extremely excited about such a possibility. They needed permission from the team's leader, Lev Gor'kov, who agreed to our pleas after a delay of a couple of days. As a result, the four of us went by car speeding along the western highways, the Russians taking pictures of the group at every opportunity, and buying and sending postcards home from every town we stopped at. Shirley had very presciently insisted that we make hotel reservations in advance by phone -it never occurred to me that we were a somewhat odd bunch, at least for folks in southern Utah -an African-American lady scientist, an Asian Indian, and two Soviets!
Besides the US-USSR workshop, in 1977 ACP had a program on turbulence, which attracted several scientists in hydrodynamics and soft condensed matter, including the discoverer of chaotic behavior in nonlinear dynamics, Ed Lorentz, and young rising stars David Nelson and Eric Siggia. With the exceptionally large activity in 1977, it was natural to expect the following year (1978) to be somewhat quieter for condensed matter. Nevertheless, two workshops took place -one on superfluidity in He and in two dimensions, and one concentrating on phase transitions and applications of renormalization group methods. The former attracted theorists (e.g. Vinay Ambegaokar, Gordon Baym, David Nelson, Lev Pitaevskii, Peter Young), computational theorists (Geoffrey Chester, Malvin Kalos) as well as experimentalists (Bob Hallock, John Reppy) from the Helium community. The latter was attended several top practitioners of the field including Douglas Abraham, Michael Fisher, Pierre Hohenberg, Leo Kadanoff, Mike Kosterlitz, Alan Luther, Barry McCoy, David Nelson, and Doug Scalapino, as well as by many others wanting to learn. The two pillars, Elihu Abrahams and David Pines were present through both programs.
1979 saw a further broadening of the scope of Condensed Matter programs at ACP, to Topological Defects and to Systems far from Equilibrium. Clearly, Condensed Matter at Aspen was coming of age by the late 1970s. Contrary to the way ACP had functioned in other areas, with a relatively loose structure, what seemed to be most attractive to the physicists in the relatively broad field of condensed matter, was the existence of well-defined workshop themes, where experts could come to discuss, and other interested participants, especially younger physicists, could come to learn about new fields in a manner not possible at their home institutions.
Before the decade ended, came another startling discovery in the field of disordered systems. Taking Thouless' ides that conductance (rather than conductivity) was central to the problem of localization to a higher realm using ideas of scaling, the so-called "gang of four" (Abrahams, Anderson, Licciardello and Ramakrishnan) showed the absence of metallic behavior for noninteracting electrons in two dimensions. This set the stage for many exciting discoveries for the next decade, and for the role of ACP programs in their development, which is described in the next section.
Phase II. Condensed Matter Comes of Age: Aspen in the 1980s - an unprecedented decade of New DiscoveriesThe 1980s witnessed a series of exciting discoveries in condensed matter physics, and with it, a continuing rise of the presence of the field at ACP. Condensed matter, unlike particle physics and astrophysics, is a more diffuse subject that has several areas of emphasis. However, ACP's success in the other fields depended on a core set of scientists; such a selection in condensed matter necessarily meant a de facto selection of a subset of areas of which condensed matter was comprised. Fortunately, one of the central figures among the ACP scientists was Phil Anderson, who was the undisputed intellectual leader of physics research at Bell Laboratories, the largest condensed matter group in the world. As a result, Phil had been involved in a wide range of topics in the field. Thus a two-pronged attack was arrived at: concentrate on a few key areas at the forefront of condensed matter, but, in addition, be inclusive by having other areas represented through focused workshops concentrating on recent advances of interest to the community as a whole. The key areas were determined by the physicists who were sufficiently committed to the ACP and to the growth of condensed matter in its programs.
As a result, ACP continued, on the one hand, to broaden its appeal to the condensed matter community during the first half of the decade, with programs on different aspects of this wide-ranging field, e.g., one-electron physics (1980), incommensurate matter (1983), and interfacial physics (1984), in parallel with programs based on major new advances in key areas at the forefront of the field as a whole. At the same time, the increased participation by a central group of condensed matter theorists led to greater representation on the Scientific Advisory Board of the ACP. Their numbers grew almost fourfold, as more condensed matter physicists got inducted as member-trustees with each passing year during the 1980s: Sebastian Doniach (1980), Patrick Lee (1981), Richard Prange (1982), David Thouless (1982), Daniel Fisher (1984), Duncan Haldane (1984), Michael Cross (1986), Pierre Rothenberg (1987), Daniel Stein (1987) and Ravin Bhatt (1988). Such a dramatic increase was only possible because of the unique combination of facilities that ACP offered -(i) a spectacular setting in which physicists could discuss at length, and (ii) a flexible format to the workshop program, so physics could be appropriately mixed with pleasure -be it hiking in the mountains, listening to great music from the Aspen Music Festival, having picnics, playing games or dining in town. Families with children also found Aspen full of enjoyable things to do, and the weather was, more often than not, perfect for family activities. Very often physicists were known to take a quick hike on one of the nearby trails in the morning and return in time for an afternoon seminar.
Given all the activity at the turn of the decade resulting from the scaling approach to localization by the gang of four, it was natural to have a summer program devoted to the physics of localization in 1981. However, as was characteristic of ACP programs, with their freestyle format (especially in those earlier days), many participants were having detailed discussions on the problem of localization and interaction effects in disordered systems the previous summer as well. Both Abrahams and Anderson (two of the gang of four) were central to Aspen's condensed matter effort at the time. Thus, a fair fraction of the activity in the field was emanating from the discussions and interactions among physicists at Aspen during those summers. Several theorists including Elihu Abrahams, Patrick Lee, Gabriel Kotliar, Claudio Castellani, Dietrich Belitz and Ted Kirkpatrick spent several summers at ACP, discussing and working on constructing a true scaling description of the metal-insulator transition in disordered electronic systems, in parallel with similar efforts elsewhere, such as Sasha Finkelstein in the Soviet Union, and Claudio Castellani & Carlo DiCastro in Rome. In parallel, Milovanovic, Sachdev and Bhatt showed that certain experimental results on thermodynamic properties in doped semiconductors were more consistent with the emergence of local moments, which were missing from the standard scaling description. Many of these issues continued to be discussed and debated by these scientists (independent of whichever workshop was officially going on), using the freestyle format of the Aspen summer programs.
Other major discoveries in quantum condensed matter physics in the early 1980s included the integer and fractional quantum Hall effects (QHE), in 1980 and 1982 respectively. Each of these spectacular and completely unforeseen discoveries garnered a Nobel prize, with German experimentalist Klaus von Klitzing receiving it for the integer QHE in 1985, and three US-based physicists, theorist Robert Laughlin, and experimentalists Horst Stormer and Dan Tsui (a frequent ACP participant), sharing the award for the fractional effect in 1998.
The sociology surrounding the discovery and development surrounding QHE was unlike any other condensed matter phenomenon. Experimentally, it required extreme low temperatures, high magnetic fields, and ultra-clean semiconductor heterostructures; very few places in the world had access to all three. From a theoretical viewpoint, it was remarkable -perfect quantization of resistance, at a level (better than a part in a billion). This was unheard of in condensed matter! Clearly, a new principle was at work, and Laughlin alone came up with the insight that uncovered the fundamental principles for both cases, using a particularly ingenious variational ansatz for the many-body wavefunction to understand the fractional QHE.
While Laughlin's original work was done elsewhere, the ACP workshops and participants were heavily involved in the developments that followed. The first of many summer programs on the subject took place in 1984, organized by Duncan Haldane, who had shown how to create a hierarchy of fractional quantum Hall states. One of the burning questions at the time was the role of disorder in stabilizing quantum Hall states, and several participants worked on constructing a two-parameter scaling theory of the quantum Hall effect. A pioneering paper emerged out of the collaboration, authored by Aspen participants Bob Laughlin, Marvin Cohen, Mike Kosterlitz, Herb Levine, Steve Libby and Ad Pruisken. QHE was a prominent topic at workshops as well as in informal discussions for several summers in the late 1980s, on aspects ranging from transport in the QH regime, and the relation to the scaling theory of localization, to topological aspects of the QHE. Collaborative work involving Arovas, Bhatt, Haldane, Thouless and others, led to a greater understanding of wave-function topology, Chern integers in the integer QHE, and its connection with the universal, localization length exponent in the QH regime for non-interacting electrons. Subsequently, the Chern-Simons field-theoretic approach to the fractional quantum Hall effect was featured in several summer workshops and also in discussions at ACP in the early 90s, involving Steve Kivelson, Shoucheng Zhang, Dung-Hai Lee and others. These developments can properly be considered as precursors to the extensive activity in condensed matter physics on topological insulators, which became prominent after 2008.
The only theorist among the QHE Nobel prizewinners, Bob Laughlin, attended ACP during the summers of 1982 and 1984; a decade later, he also served as a General Member of ACP for ten years. One of the experimentalists, Dan Tsui found the atmosphere at Aspen so conducive to interactions with theorists that after organizing a program in 1990, he has participated in the summer program in fourteen of the last sixteen years.
While much of the quantum condensed matter community was engaged in the study of disordered electron systems and the quantum Hall effects, the rest of condensed matter saw a resurgence in the study of nonlinear classical fluids, especially pattern formation and the route to chaos as an accumulation point of bifurcation transitions. Under the leadership of ACP board members Pierre Hohenberg and Michael Cross, several summer programs such as the one on Pattern Formation in 1986 and Spatially Extended Non-equilibrium Systems in 1989 explored these issues in some depth, by bringing together leading physicists and applied mathematicians in nonlinear fluid dynamics. In addition, Tom Lubensky and Phil Pincus organized a workshop on Complex Fluids in 1988, which attracted many physicists working in soft condensed matter.
Much of the research in spin glasses in the half-decade following the activities at Aspen in the summer of 1976 were carried out in Europe both on the analytical and numerical fronts. Following that, however, US researchers joined in two major quests - do real three dimensional spin glasses have a genuine thermodynamic phase transition like the SK model, and further, how much of the intricate, hierarchical behavior seen in the mean-field model applies to them? In 1984, two sets of researchers -Ogielski, and Bhatt & Young independently used Monte Carlo methods to demonstrate that 3D Ising spin glasses underwent a genuine phase transition, like the mean-field model; this was soon confirmed by Singh and Chakravarty by series expansion methods. On the other hand, renormalization group treatments by McMillan, Bray & Moore, and Fisher & Huse suggested a somewhat different picture of the low temperature phase of 3D spin glasses than the hierarchical scenario obtained in mean-field results. In light of the above developments, Daniel Fisher, Daniel Stein and Richard Palmer organized a workshop in summer 1985 entitled "Glassy Dynamics". Gathering together active researchers in the field to discuss the new results, this workshop set the agenda for the new frontier of glassy dynamics. Much of the work started as a result of the discussions at this program was continued at subsequent longer programs at the Institute for Theoretical Physics in Santa Barbara in fall 1986 and again in the 1990s, where several of the same scientists participated. Thus, research sparked by ACP activities went on in the US for the rest of the eighties and was carried to fruition by researchers in Europe during the following decade.
Computer access at the ACP during the first 20 years had been rudimentary; one could say, for the most part, non-existent. This was looked upon almost as a matter of pride - participants at the ACP took advantage of the lack of communication facilities during their weeks at Aspen to rid themselves of mundane daily tasks, and think about weighty and important research problems. However, it was precisely the lack of communication that kept computationally oriented researchers away. In 1987, ACP saw its first computationally oriented summer program in condensed matter -on Monte Carlo methods, organized by David Ceperley and Jorge Hirsch, which attracted some of the top computational scientists in the field. In the following decades, with the advent of the PC revolution, ACP yielded to better computer communication and broke its isolation, and more computationally oriented programs were organized, involving the leaders in that realm of condensed matter and other physics disciplines.
By the mid 1980s, ACP expanded its efforts beyond the summer program to include week-long workshops in the winter. These were designed to be short, but requiring a shorter lead-time, so latest developments could be included. The first such Aspen Winter workshop was in particle physics in 1985; condensed matter followed the following year with a week-long workshop of its own. The timing could not have been more fortuitous, for in late 1986, condensed matter received perhaps its biggest bombshell in the latter half of the twentieth century -the discovery of high temperature, oxide-based superconductors. Bednorz and Muller, who originally found superconductivity in a cuprate, lanthanum copper oxide, with a transition temperature about 50% higher than the previous record holders, (the A-15 compounds), received the Nobel prize in 1987. However, within a matter of months, related cuprate compounds were synthesized that raised the superconducting transition temperature to over 90K, a factor of four larger than the A-15s. The ACP has been able to respond rapidly to timely developments in condensed matter physics and in response to this unprecedented discovery, the winter workshop at Aspen in early 1988 was devoted to the subject of high temperature superconductivity.
This one-week long conference brought theorists and experimentalists together to confront the latest results. Among these was the striking report of Birgeneau that the parent lanthanum cuprate compound has an antiferromagnetically ordered ground state and that the spin correlations follow precisely the newly developed unpublished theory of quantum antiferromagnetism of Chakravarty, Halperin and Nelson (which was developed into a highly cited paper the next summer at ACP by Chakravarty). Various attempts to arrive at a theoretical understanding of the high-temperature superconductivity were reported. Many leading theorists, both in condensed matter, and outside, joined the fray. Unlike the spectacular success that had been witnessed for the quantum Hall effect, this time a proper understanding was not immediately forthcoming. On the contrary, during the first few years, even the basic mechanism was not, and is not yet agreed upon; the number of theories grew along with the number of theorists working on the problem. The summer program seemed to be the ideal venue for dealing with such a situation, and it was decided that the condensed matter program in 1988 summer be devoted to the subject. Since the oxide superconductors were obtained by adding carriers to a Mott insulating oxide, many people felt that electron correlation effects were important. Consequently, the summer program carried the title "Correlated Electron Systems"; Ravin Bhatt and Steve Kivelson were chosen as organizers, and were charged to attract a wide variety of participants. Given the importance of the problem, this proved an easy task; however, selection of speakers was another matter, and it was felt that for best results, after a comprehensive overview given by Phil Anderson, formal talks be restricted to experimental facts, and various theoretical models be aired in informal settings, allowing full scope for critical discussion. The program attracted an unprecedented number of applicants, including many experimentalists; this set the stage for a large number of subsequent workshops dealing with this thorny but important issue in condensed matter physics at the ACP. The following year, the summer workshop was given a more focused title -"Unconventional Superconductivity", which the high-temperature superconductivity in the cuprates clearly was, as experiments began to show clearly the unusual character of the superconducting order. Progress was taking place, but it was slow, compounded by the fact that these were ternary materials and oxides were notorious for having problems with vacancies. Clearly, this was going to occupy the community for the next 5-10 years; what was not realized at the time was how much of an underestimate that was. It is worth recalling that it took almost fifty years for the BCS theory to be formulated, after the original discovery of superconductivity.
Phase III: Condensed Matter at ACP from 1990 to the presentThe discoveries in quantum condensed matter during the 1980s led to a major resurgence in advances in theoretical techniques to deal with the new challenges. The sophistication of these theoretical methods and the intellectual questions they posed attracted a whole new cadre of young, budding condensed matter theorists. Many of these looked to Aspen as a place to be during summers for new ideas; with their regular participation, Aspen became a Mecca for theoretical discourse in the field.
In parallel with the explosion in the number and quality of upcoming young theorists in condensed matter and other fields, ACP was confronted with the need to change its governance. From a situation where a few volunteers worked for the Center in the 1960s, and Trustee-members were elected for unspecified terms, the number of potential members of the Advisory Board grew significantly by the 1980s. It became an honor to be asked to serve on the Board. To avoid having a Board that was too large and unwieldy, in 1989, the ACP formed a committee to address this problem. The committee, chaired by one of the newly appointed members (Ravin Bhatt), came up with a recommendation to limit the terms of members of the Board. All former life-members were asked to resign effective the summer of 1990, and many were re-elected with staggered terms ending in 1-5 years. For condensed matter, this change was not only healthy, but also necessary, given the large number of promising recruits who were young and energetic. They could be expected to carry on the efforts of their predecessors with enthusiasm, and hopefully with foresight as well. The rules were flexible enough to permit dedicated members to continue with an honorary status, which allowed them to participate as non-voting members of the governing body. Needless to say, the nineties saw many new condensed matter board members, including the first women members in the field -Susan Coppersmith, Catherine Kallin, Barbara Jones, Karin Rabe, and Premala Chandra.
Along with the new constitution, the ACP found itself urgently needing an upgrade of its facilities. Hilbert Hall, which had been built with a finite (short) timeframe, needed replacing. A campaign was organized, in which A. Douglas Stone, a Condensed Matter ACP Board Member, played a crucial role. The result was a much-improved facility, Smart Hall, with the attached new auditorium, the Flug Forum, several discussion areas, and many more offices than before. With the new facilities, the nineties also saw a significant rise in applications to ACP, which, in turn, led to an increased formalization of the procedure for selecting workshops, as well as selection of applicants, requiring greater diversity and priority for fresh, deserving applicants. All this worked well with the ever-increasing numbers of condensed matter theorists who were applying to attend ACP programs, both in the summer as well as in the winter season.
For condensed matter physics, the nineties at Aspen, as elsewhere, could be called the decade of correlated electron systems. While there had been a very strong presence of correlated systems physics at Aspen from the first days of condensed matter, e.g. helium (60s-70s), and Heavy Fermions (70s-80s), the issue rose to unprecedented prominence with the discovery of high temperature superconductivity in the cuprates. Condensed matter physicists all over the world were attracted to the promise of high temperature superconductivity, as bees to honey. Superconductivity at room temperature would lead to a revolution in technology comparable to the semiconductor revolution of the 1950s.
At Aspen, six summer programs and four winter workshops dealt with various aspects of the subject, with titles like Quantum Criticality, Non-Fermi Liquids, Quantum Magnetism, High-Temperature Superconductivity, Strongly Correlated Metals, Strong Interactions in Low Dimensions, etc. In addition, strong interaction physics in the quantum Hall regime was featured in two of the summers. The development of theoretical methods to treat strong electron-electron correlations in quantum matter continued to be the major theme. Among the new ideas that emerged and were explored in some detail in the context of strongly correlated materials were Dynamic Mean Field Theory, and slave boson and fermion methods. For the fractional quantum Hall problem, a new method for rationalizing the hierarchy of states by mapping the fractional QH problem to an integer QH problem of composite fermions was developed by Jainendra Jain, and was extensively discussed at the program in 1993, which he attended. Novel variational wavefunctions were proposed for non-Abelian FQH states. New calculational tools were developed to explore beyond the inspired variational wavefunction approach. These involved Chern-Simons Field Theory methods coupled with the Landau-Ginzburg approach, to study fluctuation effects for quantum Hall phases, and transitions between them. Field-theoretic methods had become an essential part of the condensed matter theorist's toolkit. Communication and interactions with field theorists became more common, and ACP provided an ideal environment for such interactions and collaborations. In 1993 summer, a program on Integrable Quantum Field Theories was organized, involving participants from several disciplines, including condensed matter.
As ACP participants represent various areas of theoretical physics, it is natural that often discussions result in unexpected collaborations. A case in point is the collaboration between Nick Read and Greg Moore that began at ACP in the summer of 1989 and resulted in an oft-cited path-breaking paper (1991) on exotic non-Abelian quantum Hall states. This is an example of an advance that happens without a particular workshop, and which is a result of having physicists with different expertise talking together at ACP.
Despite belonging to the generalized field of correlated electrons, high-temperature superconductivity and FQHE were very different, as their historical development shows. The QH problem was clean, and the theoretical insight, though profound, came quickly. Further, as a result of strong experimental effort, most of the important theoretical issues got resolved relatively fast. In high TC, by contrast, many properties seemed to depend on chemical details, there were competing effects, and the theoretical issues were far from clear. Descendent of the long appreciated, but never really solved, Mott problem of insulation by correlation, research in high TC required many new insights. As a result, it was natural that the topic was involved in so many workshops at ACP, starting with the earliest one in 1988, where Anderson gave a detailed presentation of his Resonant Valence Bond idea, and many others gave competing proposals. Over the next two decades, many experimental findings emerged, and most workshops involved theorists and experimentalists working together to sort the wheat from the chaff, to work out the detailed phase diagram including new phenomena such as non-Fermi liquid (strange metal) behavior, and pseudogaps. While these workshops have helped the emergence of the consensus that strong electron correlations are a notable feature of the cuprate superconductors, the theoretical understanding of high TC is still not at the level of the BCS theory for conventional superconductors.
The nineties also saw a rapid expansion in the winter workshops in condensed matter, to a level where they became an integral part of ACP's activity in condensed matter. Board members Elihu Abrahams and Sudip Chakravarty took a leading role in this development, by identifying key people to be organizers (and twisting arms where necessary), and often by organizing the workshops themselves. By the end of the decade, the task became easier, and ACP members shared the task of being on the winter workshop committee. Winter workshops were organized in several areas, such as Highly Correlated Electron Systems (1990), Future Trends in Low Temperature Physics (1992), The Physics of Reduced Dimensionality Systems (1995), Defects in Soft Condensed Matter (1998), Quantum Criticality (1999) and Fundamental Physics of Ferroelectrics (2000). The format of these workshops, though closer to conferences because of the shorter (one-week) duration, was flexible enough to accommodate the latest developments because of the shorter time from conception to implementation. For many, ACP Winter Conferences became an annual must-attend affair - the winter counterpart of the Gordon Conferences. These one-week meetings illustrate the organizational flexibility of the ACP, which enables it to respond quickly to important new developments and to contribute to setting the agenda for future work. A case in point is the 1999 winter conference with the title "Quantum Criticality". Probably this was the first time that a full conference with this title was organized. Since then this subject has blossomed to an extent that it is now widely discussed in many contexts, particularly for the heavy-fermion compounds and remarkably, in the language of AdS/CF(M)T. In the latter topic, since ACP participants come from both the condensed matter and string theory communities, it has played a unique and crucial role in facilitating a remarkable synergy between string theorists and condensed matter theorists.
Though high temperature superconductivity took a major portion of the ACP summer and winter workshops, other fields were also represented through the decade. Physics of disorder, which had figured prominently in the late seventies and early eighties, saw a program devoted to it in 1997 summer, entitled "Quantum Phase Transitions in Disordered Systems", organized by Subir Sachdev, Myriam Sarachik and Peter Young. This program dealt with the expanded field emerging from the studies in the eighties on metal-insulator transition in disordered systems. It included, in addition, superconductor-insulator transitions, as well as phase transitions in disordered quantum magnets, e.g., quantum spin glasses, a natural evolution of thermal phase transitions in classical spin glasses.
A major revolution that took place during this era was the PC revolution, and following that, the development of the World Wide Web. With physicists increasingly relying on computers both for research and for communication of research, Aspen could no longer remain isolated from the rest of the world, where "one could work in peace with nature as one's only companion". Computational access became imperative, and with it ACP became more hospitable to physicists who used computers as a major tool in their research. In condensed matter, this meant, besides electronic structure physicists, those doing Monte Carlo, Numerical Renormalization methods (such as Density-Matrix-Renormalization-Group) and the like. While ACP had hosted programs in the eighties in both electronic structure (e.g., Physics of Clusters, organized by the late Michael Schluter in summer 1986) and in Monte Carlo methods (1987), the availability of computer connections (first wired, then wireless) in the nineties really made ACP attractive to all areas of condensed matter research. More of the attendees were involved in computational research at various levels than in previous decades. Several summer programs, e.g., Materials at High Pressure (1997), Physics of Insulators (1998), and Physics of Semiconductor Lasers (1990), and a number of winter workshops broadened the scope of condensed matter physics at ACP in this period.
Towards the end of the nineties, advances in cold atom physics made it possible to address many topics of interest in condensed matter in these systems. As a direct consequence, ACP had a program entitled "Exploring Bose-Einstein Condensates" in the summer of 1999, the first of many programs devoted to this cross-disciplinary field between atomic physics and condensed matter. Another program the following year was entitled "Quantum Information and Computation", exploring the interface between quantum physics, information theory and computation, a subject which has also grown substantially in the decade that followed.
The year 2000 began with a special Winter Workshop, entitled "Fifty years of Condensed Matter Physics" held in January 2000. This workshop celebrated the (up to that point) fifty-year involvement of Phil Anderson ("PWA") with, and leadership of, the field of condensed matter physics. Given his strong connection with ACP, it was particularly appropriate that it was held as an Aspen Winter Workshop. Organized by Ravin Bhatt and Phuan Ong, two of Phil's colleagues from Princeton, it was attended at full capacity for an Aspen winter workshop, with over a hundred attendees. Seminars covered a wide range of topics "of interest to PWA" (which pretty much covers all interesting aspects of condensed matter, and beyond, to other fields of physics, biology, and computer science). Most of the seminars were included in a volume entitled "More is Different: 50 years of Condensed Matter Physics" published by Princeton University Press; it gives an idea of the wide ranging influence that Anderson has had in condensed matter, both at Aspen and elsewhere.
The new millennium saw major discoveries in new materials including two-dimensional graphene, heavy-electron metals, new "high-temperature superconductors" such as the iron-based pnictides and oxychalcogenides, as well as the development of materials exhibiting unusual quantum states characterized by topological properties such as topological insulators and superconductors. Of course, the theoretical community responded to these developments with enthusiasm and continues to do so; this is reflected by the various summer and winter workshops that have been held on all these subjects. The advances in cold atom systems continued, and even accelerated, to include optical lattices, whereby actual many-body Hamiltonians encountered in real materials could be engineered. In parallel, manipulation of spins at the nanoscale became feasible, allowing one to truly manipulate quantum information, or qubits.
As in the past, ACP responded with swiftness to the community's desire to have these new developments be part of the summer program and winter workshop agenda. Almost every summer, programs included some aspects of these new frontiers, e.g. Fundamental Issues in Quantum Gases (2001); Spins in Nanostructures (2001); Exploring the Interface Between Cold Atom and Condensed Matter Physics (2003); Coherence and Dissipation in Quantum Systems (2004); Ultracold Atomic Gases (2005); Interactions, Coherence and Control in Mesoscopic Systems (2006); Topological Phases and Applications to Information Processing (2007); Complexity, Disorder and Algorithms (2008); The Physics of Graphene (2008); Quantum Simulation and Computation with Cold Atoms and Molecules (2009); Low Dimensional Topological Matter (2010); Few- and Many-Body Physics in Cold Quantum Gases (2011); and Iron Pnictides and Beyond (2011). Many winter workshops were devoted to these new areas, such as Quantum Coherence and Dissipation (2002), Spins in Nanostructures (2004 and 2007) and Strong Correlations in Ultracold Fermi systems (2006).
In parallel, ACP continued to have both summer programs and winter workshops in its core areas of correlated and disordered systems, as well as in soft condensed matter. A program involving both communities was organized in the summer of 2002, entitled "Collective Phenomena in Disordered Insulators and Glassy Systems", allowing the two groups to interact and learn from recent developments in each other's field. New areas of research in soft matter such as Packing problems and Jamming were featured in summer programs in 2006 (Physical and Mathematical Aspects of Packing), 2007 (Jamming) and 2008 (Interfaces, Topological Defects and Flexible Packings). Summer programs in the past couple of years in soft matter have been on "New Perspectives on Strongly Correlated Electrostatics in Soft Matter" (2010) and "Fluctuations and Response in Granular Materials" (2011).
It is almost always the case that discussions at the ACP workshops in condensed matter physics result in the identification of research topics that offer great opportunities for the next years. For example, new ideas at the 2005 workshop on Ultracold Trapped Atomic Gases included collective modes in superfluids near Feshbach resonance and quantum spin dynamics in optical lattices. Similarly, the 2007 workshop on Topological Phases found topics for future emphasis; among them were theory of topological phases and transitions between them, structure of fractional quantum Hall states, non-Abelian topological order, anyon models, and characterizing topological order with entanglement entropy.
Clearly, the last two decades have seen an improvement in both the quality and quantity of the ACP programs in condensed matter (both summer and winter), and of the participants that contribute to its success. Thus, the numbers of publications in premier journals that acknowledge ACP continue to rise. (For example, during the first decade of the new century, the number of papers in only APS journals, Physical Review and Letters, which acknowledge ACP, was over a thousand, of which a majority was in condensed matter). Such progress augurs well for the future.
SOME CONCLUDING THOUGHTS -In summary, the Aspen Center for Physics has been transformed from a Center where a few distinguished physicists gathered together to discuss problems of interest to the physics community half a century ago, to a true physics Mecca today, where physicists of all stripes gather and exchange ideas on an annual basis. In Condensed Matter Physics, this has been a true success story. ACP has hosted almost half the Nobel Prize Winners in the field. Some of them have come repeatedly, and a few have been involved as ACP Board Members and Officers. Of these, Phil Anderson deserves special mention, having been intimately involved in channeling efforts in key areas of research from the vast field that condensed matter represents.
In addition, ACP's success is due in no small measure to the dedication of several leading condensed matter theorists to the task of making condensed matter a central part of the activities of ACP. Their hard work, and the consequent success, drives the enthusiasm with which new researchers have taken on the mantle; this bodes well for the future of Condensed Matter at ACP. If there is one lesson for ACP members, it is the following: selfless dedication to centers of excellence like ACP may at times seem like a thankless task, but over the course of years, one realizes that the payback is several-fold in terms of a sense of accomplishment, and a legacy to pass on to the next generation, which after all is the dream of every active physicist.
As this history of the first fifty years of condensed matter physics at the Aspen Center for Physics is being written, another summer session is underway at the idyllic ACP. The program, from its description, and the quality of the attendees, promises to be as dynamic and effective as programs in the past years, perhaps even more. The comments ACP receives at the end of every participant's stay wax eloquently about the influence their interactions at ACP have on their research in the near future or in the long-term. Based on these, ACP's programs have been an unqualified success, and one that the condensed matter community is very privileged to be able to experience. Of course, the science is of their own making; but the atmosphere with the mountains all around, the wonderful music coming daily from the nearby music tent, the incomparable weather that Aspen to offer, all do play their part in making it an experience that is hard to forget. For that, and the part that the local community has played in making it possible, the condensed matter community will be forever grateful.