Glimpses of Greatness∗ a Personal View of P W Anderson (1923–2020)

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Glimpses of Greatness∗ A Personal View of P W Anderson (1923–2020)

G Baskaran

P W Anderson was a theoretical physicist. He won the No- bel Prize in 1977. He catalysed Nobel Prizes for several others. His career spanned 72 years of relentless research, filled with path-breaking contributions. He focussed on ‘here and now’ phenomena of inanimate materials and built theoretical quantum models of lasting value. He communed with nature by contemplation and study of experimental results. As a G Baskaran is a theoretical founding father, he set agenda for the field of condensed mat- physicist. He studies a variety ter physics, for half a century. It is a growing fertile field now, of quantum phenomena, with a web of connection to different corners of science, tech- including theory and nology, and sometimes beyond. As a person, Anderson was mechanism of room-temperature remarkable. He was my long time collaborator since 1984. I superconductivity. He shares had a wonderful opportunity to join hands with him when he his time between The Institute initiated the resonating valence bond (RVB) theory of high- of Mathematical Sciences, temperature superconductivity in cuprates in early 1987. Chennai, Department of Physics of Indian Institute of It was 1986. I was talking to Anderson in his office at Prince- Technology Madras and ton. A young undergraduate walked in. Students knew that no Perimeter Institute for Theoretical Physics, prior appointment was necessary to meet this Nobel Laureate in Waterloo, Canada. his office. The student elaborated on an idea he had. After a while I became impatient. Anderson patiently listened till the end; he did notice my impatience. After the student left, Anderson en- lightened me, with his own understanding of a very important point that the student was actually trying to convey, but didn’t completely succeed. I woke up. On several occasions, Anderson brought out deep meanings in very ordinary sounding seminar talks and pleasantly surprised the speaker and audience. Keywords Condensed matter physics, RVB There was another side to Anderson. He called himself ‘a thought- theory, high-Tc superconductivity, superfluids, Higgs Particle, science of complexity. ∗Vol.25, No.5, DOI: https://doi.org/10.1007/s12045-020-0979-x

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ful curmudgeon’. Curmudgeon means a ‘bad-tempered old person’. Bad-tempered he could be; but that was often common to senior established scientists, who were pompous but simplistic, who won their way, and sometimes misguided the scientific community. In his Scientific American article on Anderson—‘Gruff Guru of Physics’—John Horgan states, “Robert Schrieffer, a No- bel Laureate in physics who has often butted heads with Ander- son, admires his blunt style. Anderson “has played a uniquely provocative role to make sure that people get things right,” Schri- effer says. But he adds that Anderson can be undiplomatic.” Science has witnessed outstanding scientists, who change the course of science. Such individuals are remarkable and unique in their own ways. They offer us a feel for the wonderful world of science and show us ways to practice science and get friendly with it. One such person in the field of physics was P W Ander- son, who passed away at the age of 96 on 29th March 2020, at Princeton, New Jersey, USA. He was connected to several scientists of Indian subcontinent origin: T V Ramakrishnan, B S Shas- try, H R Krishnamurthy, V N Muthukumar, K Muttalib, Sanjoy K Sarkar, Sudip Chakravarty, C M Varma, G Srinivasan, Ravin Bhatt, Anil Khurana, Sajeev John, Shivaji Sondhi, Mohit Rande- ria, Nandini Trivedi, and others. In his personal and advisory ca- pacity, Anderson supported the growth of the International Center for Theoretical Physics (ICTP), Trieste, Italy and helped in dis- seminating theoretical physics to the Third World countries, in their formative periods. Anderson was also a long time Foreign Fellow of the Indian Academy of Sciences.

Anderson’s As a theoretical physicist, Anderson looked at the beautiful, com- mathematical analyses plex, dirty, and daunting inanimate matter of all kinds; from rust were guided by physical (magnetic oxides of iron called Mott insulators), gems, and su- intuitions and the repeated use of perconductors to superﬂuids in the crusts of neutron stars. He experimental results. He handled them skillfully by building mathematical models; most coined the term of them quantum mechanical. Interestingly, his entire career was ‘condensed matter built on the proper and eﬃcient use of the body of available ex- physics’. He had an eye and passion for biology perimental results. His mathematical analyses were guided by but was too preoccupied physical intuitions and the repeated use of experimental results. with inanimate matter.

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Figure 1. Professor P W Anderson (left) with the author. The photo taken on 13th December 2018, the 95th Birth Day of An- derson. He drove from home. The Physics Depart- ment surprised him with a birthday cake. We are re- laxing after our usual arguments, disagreements, and laughter. (Image courtesy: G Baskaran) He coined the term ‘condensed matter physics’. He had an eye and passion for biology but was too preoccupied with inanimate matter. He, however, inspired several others into biology. When I invited him to visit India, about 10 years ago, he said he was avoiding long-distance travel, to focus on some of his unfinished ideas in biology. Anderson was awarded the Nobel Prize in Physics in 1977 along with Sir Nevill Mott and John van Vleck. It was a wonderful combination: van Vleck was Anderson’s PhD thesis supervisor. Nevill Mott was an admirer of Anderson, who nurtured Ander- son localization theory and applied it to amorphous semiconduc- tors. The Nobel citation stated, “for their fundamental theoretical investigations of the electronic structure of magnetic and disor- dered systems.” His body of contributions deserves, according to many, a few more Nobel Prizes. More importantly, his works and insights paved the way for several Nobel Prizes for others. Condensed matter physics is a less attractive corner of physics to fresh young minds. For many, it is dull, boring, and not fundamental enough. However, insights that these down to earth problems offer into the inner workings of nature at different scales (below earth scale and beyond earth scale), are unfathomable. Two examples are (i) Anderson–Higgs mechanism [1] of the mass generation of elementary particles, which came from theoretical insights into superconductivity, and (ii) glitches in pulsar periods,

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as arising from neutron star quakes driven by vortex creep in the crust containing the neutron superﬂuid [2].

Various factors shape a Various factors shape a person as a successful scientist when he person as a successful grows up. Often it is a teacher who inspires. Families also nurture scientist when he grows the free spirit and a spirit of inquiry. In his Nobel Prize biograph- up. Often it is a teacher who inspires. Families ical note, Anderson says, “At Illinois, my parents belonged to also nurture the free a group of warm, settled friends, whose life centered on the out- spirit and a spirit of doors and in particular on the “Saturday Hikers”, and my happiest inquiry. hours as a child and adolescent were spent hiking, canoeing, va- cationing, picnicking, and singing around the campfire with this group. They were unusually politically conscious for that place and time, and we lived with a strong sense of frustration and fore- boding at the events in Europe and Asia.” Anderson goes on, “An important impression was my father’s one Sabbatical year, spent in England and Europe in 1937. I read voraciously, but among the few intellectual challenges I remember at school was a first-rate mathematics teacher at the University High School, Miles Hart- ley.” Anderson went on to Harvard and finished his undergraduate studies in physics, with a good record. He finished his PhD at Har- vard. According to him “Graduate school (1945–49) consisted of excellent courses; a delightful group of friends, centered around bridge, puzzles, and singing.” Joyce Gothwaite became his life partner, and Anderson had 73 years long life journey with Joyce. They were a wonderful couple and great hosts. Joyce was a great support for Anderson. Their daughter Susan was born in 1948. Beyond observation of Nature and experimentation, conceptualization and model building are very important for science. Our ancestors had models for the solar system and models for the uni- verse. Model building is part of human activities. Ancient medic- inal systems such as Siddha, Ayurveda, and Unani have models for diseases in terms of imbalances in competing phenomenolog- ical components. In our personal lives, we build our own mental models (sometimes wrong) about people whom we interact with. We categorize, make hypotheses, judge, and also anticipate (pre- diction). Such qualitative considerations abound in human activ-

620 RESONANCE | May 2020 GENERAL ARTICLE ities.

Mathematical model building for physical and chemical proper- Mathematical model ties of inanimate matter is relatively simpler than for biology. For- building for physical and tunately, the dividends are also high. It gives condensed matter chemical properties of inanimate matter is physics its quantitative and predictive power, despite the com- relatively simpler than plexity and variety it faces. The ability to do controlled experi- for biology. Fortunately, ments is an organic part of this activity; nature and experiments the dividends are also become a powerful force in model building, guide our imagina- high. tion and help create new/relevant mathematics. To an outsider, Anderson’s contributions are a less appealing, technical looking, and a very specialized collection—theory of spectral line shapes and pressure broadening, quantum theory of antiferromagnetism, superexchange theory, the model for dou- ble exchange, frustrated magnetic systems, the theory of localization of waves in random media, the pseudospin formalism of superconductivity, the theory of neutral superfluids, theory of local magnetic moment formation in metals, Kondo effect, spin glass theory, poor man’s renormalization theory, the theory of or- thogonality catastrophe, resonating valence bond (RVB) theory of high-Tc superconductivity, tomographic Luttinger liquid, hidden Fermi liquid, etc. What was remarkable was that almost all of the above were thoughtful reactions to a body of experimental results, concerning unusual phenomena, correlations, and universal properties, which often went unnoticed by the community. It is indeed remarkable that each of the above contributions of Anderson flourished into a new field in condensed matter physics, and sometimes beyond. When one encounters the complex nature and tries to understand parts of it, it is important to have a clear idea of what one is trying to do. This is the beginning of the formulation of a problem— conceptualization, identifying key ingredients, setting aside irrel- evant variables. It is often an art, rather than science. It involves contemplation and imagination, within the limits and constraints set by the real world. At the same time, use the wealth of experimental results available. Anderson excelled in model building

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and finding solutions to the mathematical models he built. An- derson was a sculptor of quantum models. His chisel and hammer were experimental results and deep contemplation. In January 2000, Aspen had a workshop honoring Anderson’s 50 years of contribution to condensed matter physics. Many of An- derson’s collaborators spoke. Before I began my talk, I told the audience that I would reveal the secret of Anderson’s success. Anderson, who was in the front row, raised an eyebrow. I said that Anderson kept looking at a body of experimental results till he found the right model. My next sentence surprised the audience and got a smile from Anderson. While everyone would try to solve his or her model using mathematical methods, analysis, approximations, etc., Anderson would go back to experimental results. Experimental results guided him to guess the right solution to the model. This meeting also brought out another aspect of Anderson—how he has often guided experimentalists to the right path. Doug Osheroff and Dan Tsui, both Nobel Prize winners spoke at this meeting. Doug, as a graduate student from Cornell, was per- forming his low-temperature experiments with liquid helium-3. He found some glitches in his ultra low temperature data. His supervisors at Cornell were not impressed by the glitches and thought that it was an experimental artifact, When Doug joined the Bell Labs, he showed the data to Anderson, his eyes lit. He was supposed to have said, “Go and repeat the experiment, it in- dicates the presence of a superfluid phase transition, predicted by Anderson–Morel theory”. Doug found that it was indeed a phase transition. Rest is history: Doug Osheroff shared a Nobel Prize for this discovery with D Lee and R C Richardson. On a morning in 1996, when Doug Osheroff’s Prize was announced, Anderson came running to my office, nearly singing and dancing that Doug got his Prize. Incidentally, Tony Leggett’s Nobel Prize in Physics (2003) is also intertwined with Doug’s discovery and Anderson– Brinkman–Morel (ABM) and Balian–Werthamer (BW) phases of superfluid He3. The next talk was by Dan Tsui. Impressed by the experimen-

622 RESONANCE | May 2020 GENERAL ARTICLE tal discovery of integer Hall effect, a remarkable quantization of an electrical (Hall) resistance, Dan Tsui at Princeton wanted to go deep into it. He prepared better samples and made Hall measurements. He saw the beginning of an additional plateau in his resistance measurements, below the first integer Hall plateau. He wasn’t sure and went to Anderson and showed him the data. An- derson’s eyes lit up and he said, “Go and repeat the experiments, there is something important there.” That was the beginning of the fractional Quantum Hall effect, which got the Nobel Prize for the experimentalists Dan Tsui, Horst Stormer, and theorist Robert Laughlin. There is also another story—it was Anderson who first appreciated Laughlin’s theory of integer and fractional quantum Hall effects, while others weren’t sure. Anderson believed in the importance of thinking in generalities. While at Bell Labs, as a young staff member, his boss Bill Shock- ley requested Anderson to do some detailed calculations on some of his ideas on BaTiO3, a ferroelectric. Anderson says, “...soon I became more interested in generalities, feeling that calculations were premature”. This is an important lesson in doing science. This is an important While acting locally, one should not forget to think globally. Once lesson in doing science. he remarked to a friend of mine, “the problem is you start calcu- While acting locally, one should not forget to lating before you start thinking”. I have also heard the remark, think globally. “you should think before you ink”. In those years, before the 1990’s, when Anderson traveled widely and attended conferences, condensed matter community was al- ways looking for Anderson’s presence at the conferences. Appar- ently, it made a difference and enlivened the conference, mostly because of the discussions with him on conference talks and other topics. It is also said that, if there was a new discovery in condensed matter physics, Anderson’s involvement will make a sig- nificant difference and often direct the discovery into fruitful di- rections. In the famous APS March meeting at New York in 1987, my friend Hide Fukuyama made a thoughtful remark, after An- derson presented his talk on the RVB theory of high-Tc superconductivity. It was all new. Fukuyama remarked, “It is good Phil Anderson has entered the field and insists that it is different

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and is opening a new direction. Otherwise, people would have found some easy solution and wrong theory and closed the ﬁeld”. During a summer month, in the late 1980’s at IBM Research Lab, York Town Heights, NY, (late) Ted Schultz told me the fol- lowing story. Bardeen–Cooper–Schrieﬀer (BCS) theory had just come out. It was getting popular, but not completely accepted, partly because of the gauge invariance issue. News of BCS theory reached Pauli in Switzerland. He was quick to ask what young Phil Anderson felt about it. The answer was that Phil Anderson was excited about it and was working on it. Pauli is supposed to have remarked, “Then BCS theory must be correct”. In 1958, just ten years after his PhD, young Anderson was supposed to have made deep impressions on people like Pauli, and also people at Landau Institute. In was the summer of 1978 I think. I was visiting Zagreb Uni- versity at former Yugoslavia for a week from ICTP, Trieste. I had gone to ICTP for a summer workshop from IISc Bangalore, where I was an Institute Fellow. It so happened that Lev Gorkov from Landau Institute was also visiting Zagreb. We stayed at the same guest house. We had several discussions on condensed matter physics, stories about Landau and so on. Once he remarked, we at Landau Institute have the highest respect for the physics of Anderson, perhaps after Landau. I was pleased. Anderson was also my hero, thanks to Rajaram Nityananda, K P Sinha, (late) N Kumar, and (late) S K Rangarajan, who introduced me to Ander- son’s great works at IISc, Bangalore (1970–1978).

Anderson’s work had Anderson’s work had far-reaching implications in other fields of far-reaching implications science and even economics. In the 1970’s, the field called spin in other fields of science glass took off experimentally. Several experiments showed that a and even economics. ppm amount of magnetic impurities such as Mn, added to coinage metals like Cu, Ag, Au resulted in unusual magnetic phenomena at low temperatures. It was clear that the dilute concentration of spins of Mn atoms were communicating among themselves and freezing into some non-ordered or glassy configurations of randomly directed magnetic moment vectors. Edwards and An- derson introduced a model, with minimal and irreducible com-

624 RESONANCE | May 2020 GENERAL ARTICLE plications, to understand what is going on. They solved it using physics guided mathematical tricks. Key ingredients were competing interactions, which prevented the attainment of unique equilibrium spin states at atomic scales, resulting in a hierarchy of exponentially large number of vacua or ground states and also a genuine finite temperature phase transition. In Anderson’s world, the name of the game was frustration. John Hopfield, an ex-condensed matter Very soon, the scientific community, particularly physicists who theorist and a friend of were working on biology and other fields, saw the relevance of Anderson, then at this model to their own problems at the level of generalities. John Caltech, partly inspired Hopfield, an ex-condensed matter theorist and a friend of Ander- by Anderson spending some sabbatical months son, then at Caltech, partly inspired by Anderson spending some there, applied the spin sabbatical months there, applied the spin glass model to coupled glass model to coupled neurons in the brain and discovered the ‘spin glass like neural neurons in the brain and network model’. It is fair to say that it began a revolution in the discovered the ‘spin glass like neural network connectionist approach to understand brain functions and parts of model’. the brain. I have had an enjoyable discussion on neural networks with my former colleague (late) R Vasudevan and continue to do so with colleague Ramesh Anishetty at Matscience, Chennai. In the modern context, a layered, rather than a random network, is closely related to the popular deep learning algorithm and ma- chine learning. Anderson himself, along with D S Rokhsar and D L Stein applied the spin glass model to pre-biotic evolution. In the summer of 1983, Anderson gave a colloquium on the above topic at ICTP, Trieste, Italy, where I was on an extended visit. I had some com- ments on Anderson’s talk. My host Erio Tosatti, who knew that I was Anderson’s fan, forced me to meet Anderson and talk to him. To overcome my shyness and fear, my friend Arun Jayannavar of the Institute of Physics (IOP), Bhubaneswar, accompanied me. That was a memorable encounter with Anderson. It ended up my spending three years at Princeton (1984–87), as a visiting Assis- tant Professor at Anderson’s group. The late 1980’s were also the beginning of the complexity theory and the application of ideas of statistical mechanics and spin glass to complex optimization problems to a variety of problems,

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Figure 2. Anderson’s Gar- den. Anderson’s varied contributions to Science—in the eyes of a colleague in 1983 (name unknown).

from graph partitioning problem to traveling salesman problem, so-called the NP-complete problems. Even though we wrote a joint research paper, ‘Statistical Mechanics of Traveling Sales- man Problem’, on a specific problem, it was very clear to me that Anderson’s mind was on generalities and wanted to prove general theorems, and plant seeds for the field of science of complexity. Personally, I was fascinated by the complexity of the brain. Dur- ing my 3 years of stay at Princeton, I spent nearly one full year learning neurobiology, with an idea to get into theoretical neuro- science. Anderson strongly supported my efforts. However, in early November 1986, our attention was diverted by a milestone experimental discovery of high-Tc superconductivity in cuprates, by Bednorz and Muller. For the last 34 years, Ander- son was obsessed with this problem; so am I. I was in the right place, at the right time and with the right person: I joined Ander- son in the development of the RVB theory, right in the beginning, in January 1987, soon after Anderson put out his classic paper, which appeared in Science magazine in early 1987. I have described this and other fascinating aspects of my interaction with Anderson in an article ‘Random Walk in Anderson’s Garden’ (Figure 2), published in a book honoring Anderson on his 90th

626 RESONANCE | May 2020 GENERAL ARTICLE birthday [3], also as arXiv preprint. An important role played by an experimental paper by C N R Rao and (late) P Ganguly, in An- derson’s formulation of the RVB theory is also described in some details in this article. This book also has a delightful article by T Four decades of V Ramakrishnan [4], ably summarizing Anderson’s lifetime con- Anderson’s tribution. An Indian appreciation of high-Tc superconductivity is contributions, to my mind and to the mind of an excellent book Superconductivity Today by T V Ramakrishnan some, seems to be a andCNRRao[5]. warm-up exercise to solve high-Tc Looking back, it was 40 years of wonderful contributions to con- superconductivity densed matter physics, followed by 34 years of obsession with problem deeply and one problem, leading often to frustration and conflicts [6]. It correctly and avoid looks strange. In science there are problems, which take a long simplistic solutions. time, maturity, and collective effort, even to comprehend them. A variety of skills and different insights are needed to solve them. Four decades of Anderson’s contributions, to my mind and to the mind of some, seems to be a warm-up exercise to solve high-Tc superconductivity problem deeply and correctly and avoid simplistic solutions. My friend Sriram Shastry, while reviewing [7]

Anderson’s book The Theory of Superconductivity in High-Tc Cuprates states, “...What Anderson has given us is an integrative view of a highly complex problem, which if not actually provid- ing us with a complete solution, at the least sets the standard for the breadth of vision required of other players of the game.” I also wish to add that from the beginning of 1987, Anderson was personally a happy and satisﬁed man, like me, as far as theory and identifying the right mechanism of superconductivity in cuprates was concerned. His frustration and conﬂicts were with the high- Tc community of physicists. He remarked, when I met him last on Anderson had a full and 13 December 2018, “Baskaran, you and I understand theory and satisfying life. Beyond mechanism of cuprate superconductivity so well. I don’t know physics, he advised the US government on why others don’t understand us.” We laughed and parted. critical occasions: e.g., Anderson had a full and satisfying life. Beyond physics, he ad- stopping the supercollider accelerator vised the US government on critical occasions: e.g., stopping the to have been built in supercollider accelerator to have been built in Texas, which an- Texas, which angered gered fellow high energy physicists [8]. He was forthright and fellow high energy explained his reasons; to put it in the words [9] of Steven Wein- physicists.

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berg, a Nobel Laureate in high energy physics, “His testimony was so scrupulously honest that I think it helped the SSC more than it hurt it”. He also was part of a group at Princeton, which discussed the importance of stopping nuclear warhead prolifera- tion, star wars, etc. He had also appeared before the US Senate and presented his arguments. Anderson was concerned seriously about the human condition on Earth. Being more optimistic in these matters than Anderson, I told him in one of our conversations, “Phil, it is a matter of time, humanity will evolve into angels”. Anderson remarked, “I am afraid we may destroy ourselves before that”. The fact is Ander- son inﬂuenced so many people in his own honest and sincere ways and was a guiding light and made a better tomorrow for many and also for science. He attended to his calling as a scientist with his full might. Anderson was and is a role model.