Steven Kivelson is an American theoretical physicist who has made important contributions to condensed-matter physics. After leaving Harvard University with a PhD in 1979 and stints at the University of California, he joined Stanford University in 2004. His work has helped make sense of high-temperature superconductivity and strongly correlated systems. The latter denotes a certain group of inter-metallic compounds known for their strange electronic and magnetic properties not predicted by prevailing theories. Kivelson was recently at the Tata Institute of Fundamental Research, Mumbai, where Sounak Biswas and Prashant Kocherlakota interviewed him for The Wire.
Biswas’s and Kocherlakota’s questions are in bold and the editor’s comments are in square brackets.
The interview has been lightly edited for clarity and style. Some questions, and their answers, have been omitted from the published text because of their technical complexity.
In India, most people think of physicists as those who either study particle physics or they study the universe…
Cosmologists in particular, yes.
So what does a condensed-matter physicist do? And why is that different from what a materials engineer does?
Firstly, that is not unique to India. I think that is a widely held view of what physicists do. So, a condensed-matter physicist is actually studying materials that are available, that you can hold in your hand, that you can look at in a laboratory, which sounds much more mundane.
In general, there is no mystery as to what the fundamental laws of physics are. They are described by quantum mechanics and so we know what the basic equations are. But the solution of the equations is still unclear. The problem is still complicated… It’s almost a religious statement to say that we know what the equations are because there is no way to go from these equations to predictions of what we call ‘emergent properties’.
So what we are trying to do is to understand the connection between the fundamental laws of physics and the emergent properties of many degrees of freedom.
And what does a materials scientist/engineer do?
It’s not a question of differences in what we study, but of what our motivation is for studying and what our measures of success are. We are trying to obtain a fundamental understanding of a simple way of giving, in terms of fundamental laws, a description of emergent properties of condensed matter. A materials engineer is trying to find a material that is useful for a particular purpose.
You emphasised ‘emergent properties’ of condensed matter. Could you please explain what emergent properties are?
So, first, I would like a to advertise an article written by me with my daughter as a collaborator. My daughter is an undergrad who is majoring in philosophy. Every time I tell here about ‘emergence’, she tells me my definition of emergence is way too vague and handwavy, and so this article was an outgrowth of our discussions on this.
[Emergence is what happens when “complex behaviours that arise spontaneously from relatively simple elements” (source).]- It’s almost a religious statement to say that we know what the equations are because there is no way to go from these equations to predictions of what we call ‘emergent properties’.
In physics, I think there is a precise notion of what emergence is: it is a behaviour of a collection of objects that is qualitatively observable only in the limit of infinite number of degrees of freedom. A phase transition is an example of an emergent property. The distinction between phases of matter is an emergent property of systems. Hydrodynamics is an emergent property. All of these have a precise definition as in that you can not see phases of matter exactly in a finite number of particles.
Now, of course, we never have an infinite number of degrees of freedom. Condensed matter is always finite. But they still have a very, very many degrees of freedom, such that approximating them by an infinite number of degrees of freedom is reasonable.
Emergence is also used to mean more things. For instance, the most important to us in some sense are the emergent phenomena of life and consciousness. For we are finite, and I do not think we are willing to accept that either life or consciousness are approximate.
As a graduate student, what inspired you to take up condensed-matter physics as the subject of your PhD thesis?
When I was an undergraduate, I did not intend to be a physicist. I intended to be a constitutional lawyer. I majored in physics because it had the fewest requirements of any major. But then I fell in love with it, particularly when I took a quantum mechanics course. I have been in love with quantum mechanics ever since.
I decided to become a condensed-matter physicist in graduate school because of many reasons. But there is one particular story that maybe can serve as a proxy for what decided.
I was telling a non-physicist friend of mine that I have been learning about semiconductors, and she asked me, “What does it look like?” Now, I had never seen a semiconductor, but I told her it was shiny. I told her that because I knew that the gap was smaller than optical frequencies, so it would behave like a metal in optical frequencies.
[The gap, or the band gap, denotes the amount of energy an electron needs to jump from the valence band to the conduction band in semiconductors.]So from basic physics, I could answer a question as tangible as ‘What does it look like?’
So what brings you to India now?
I have come for an interesting conference. But honestly, I have also come because this is my first time in India. Since I was an undergraduate, I took an art history course and decided that I wanted to see Fatehpur Sikri. So this has been on my bucket list. We have been travelling for a week before this. We saw Fatehpur Sikri, we saw Agra, we saw Khajuraho, which blew my mind. The physics has been interesting as well. But this glimpse of Indian culture has been extraordinarily thrilling.
What have physicists been talking about in this conference?
The conference is high-quality physics. It is honestly just the same as a conference anywhere else. I just learned about some interesting experiments going on here that see some quantum-melting for which there really is no theory, but the data is extraordinarily explicit and precise. So that is an exciting new thing to think about.
The speakers are people I know and have talked to elsewhere for the most part. But it is a nice collection of people and it has got a gentle pace, so we are able to talk to each other.
Since high-temperature superconductors were discovered, a lot of really smart people have toiled to understand these materials. You’ve said before that everything is controversial in unconventional superconductors. How would you evaluate the status of the community in coming to an agreement on understanding these materials?
[A material’s superconductivity is the result of its electrons pairing up to behave in a way that individual electrons don’t. When these pairs form according to Bardeen-Cooper-Schrieffer (BCS) theory, they’re called conventional superconductors. Otherwise, the materials are called unconventional superconductors. Example: cuprates.]Look, condensed matter systems are very complicated. We would say there is an agreement on the mechanism of conventional superconductivity. That does not mean we understand everything about conventional superconductors. There are many things we do not understand.
- I think we have a good, basic understanding of unconventional superconductivity
For example, we have been relatively unsuccessful in predicting new conventional superconductors. At the same time, that a lot is not understood does not mean that we do not have a basic understanding.
My claim is that we have a basic understanding of unconventional superconductors as well. There are many many interesting things going on in these materials. I think we have a good, basic understanding of unconventional superconductivity, but there is an enormous amount we do not understand about the high-temperature superconductors, about the materials. They exhibit many phenomena in addition to superconductivity, and these are issues of active research and not much agreement. There is agreement but not uniform agreement.
Can you tell us a bit about how it was to work with Julian Schwinger?
[Julian Schwinger (1918-1994) was an American theoretical physicist who made major contributions to quantum field theory. He won a Nobel Prize for his work in 1965.]I haven’t. My mother was a student of Julian Schwinger’s. I knew him quite well, but I knew him as teenager. I was way too young to be his student. I know it says on Wikipedia that I was a student of Schwinger’s, but they made a mistake. That was my mother. And my mother is a very distinguished space-physicist. She is a very remarkable scientist, and was indeed a student of Schwinger’s (laughs).
What about Bob Schrieffer ?
[Robert Schrieffer is an American physicist whose name is the ‘S’ in BCS theory, the first microscopic theory of superconductivity.]I did work with Bob Schrieffer. I was a postdoc of Schrieffer’s and I worked very closely with him in the years afterwards.
What was it like to work with him?
I owe a great deal to him. He was a major mentor in my life. I had not really intended to become a physicist. I did things my own way and my thesis was all original work. That is the only good thing I can say about it. It was all my ideas, it wasn’t very good (laughs).
And then getting a postdoc position with Schrieffer and getting to understand how physics really is done – it really transformed my life. He was also incredibly generous. He would talk about things which I knew were his ideas. I mean, I worked them out, but he presented them as if it was all my work. It was embarrassing, but of course, at the end of the day, you’d know everybody knew it was his work (laughs).
He was a model of how to be generous and nurturing in science. Not only did I learn about what physics was, but he was also a model of how a physicist should live in the world.
Do you think taking up physics as a career option has changed from your time to now?
I really do not know what the answer to that is.
[arXis is the name of a preprint server maintained by Cornell University. Scientists from various fields can upload copies of their papers on to arXiv, where they are published after some moderation. The preprints thus available are freely accessible to everyone.]The arXiv certainly transformed the way physics is done. The arXiv and the internet. Remember, I was a physicist before either of these, and so it is both much more international, much faster and much more efficient. If somebody figures out how to make one move, it is immediately apparent to people all over the world, and the next move will come from somewhere else. It is just the most efficient method ever invented for knowledge generation. And that certainly has transformed physics.
arXiv has been a huge development. Some sciences have been more enthusiastic about adopting the practice of publishing preprints. Some other disciplines have been more reluctant. Any idea why this could be happening?
I can tell you the explanation they give. Theorists, as far as I can see, all post to the arXiv. Experimentalists often do not post to the arXiv or they do they wait until their articles are published.
Theorists can be more agile because there is not a huge amount of overhead. There is intellectual overhead but you do not need equipment, you do not need to grow samples and characterise them and so on.
- I would be better off from the point of view of physics with less money rather than more money.
I think that a part of it is that the experimentalists are more worried about their ideas being published by somebody else before them, but I think for most of us posting on the arXiv is publishing. So I really don’t understand it. I think they are wrong. I think everybody should take advantage of the arXiv. I think it is one of the most positive developments of our field.
Are you saying the intellectual overhead that a theorist might have is more costly than the overhead for experiments? Yeah. If a new development happens, a theorist can say, “Okay I will work on that.” You have to learn. Learning isn’t easy and as you get older it gets harder, but an experimentalist has to buy equipment, they need to be set up. So there is much more scientific inertia in doing experiments, and it is also a lot more costly. So when they get something, they better get the full benefit of it.
Also, they are small businessmen. They really have to raise money. I have to raise money, too; otherwise my students are in trouble. But honestly, I would be better off from the point of view of physics with less money rather than more money. It means I do not have to fret about money. But an experimentalist can not do their science without a large amount of funding.
In your opinion, what are the most interesting outstanding problems in condensed-matter physics right now? If you would like to know the answer to some questions, what would they be?
As long as you put it as ‘What do I feel’ – because I am uncomfortable about making a general statement about what the most interesting things in condensed-matter physics are. I can tell you what I find the most interesting.
I think there is slow but steady progress on solving some of the basic paradigmatic models of interacting electrons. You know, in the history of statistical mechanics, the solution of the Ising model plays a very big role.
[The Ising model is a way to study ferromagnetism using the rules of statistical mechanics.]Once you really understand the Ising model, you understand a lot about statistical mechanics. It is not that it is a model [of any real material].
So similarly, there are models that have been defined – simple models of electron-electron interactions like the Hubbard model, models of electron-phonon interactions like the Holstein model, models of electronic systems near quantum critical points.
But unlike the Ising model, these haven’t been solved. I mean of course the Ising model does not have an exact solution in three dimensions. But come on, we know everything about the Ising model. That is not the case with paradigmatic models of electrons.
However, there are increasingly good methods – largely numerical, but informed by advances in various ways of looking at things. And I think there is shortly going to be a body of information which says, “Look, here is the phase diagram of the Hubbard model, here is the phase diagram of the Holstein model…”, and so on. That, I think, is [going to be] a very exciting development. That means all these vague stories we have told about correlated systems can be made much more precise by analogy with these well-defined models.
In particular, the theory of quantum critical phenomena in metals. Quantum critical phenomena in insulators is just like classical critical phenomena in one more dimension.
[Critical phenomena encompass the events that happen at/or around critical points.]There is an interesting interplay of dynamics and thermodynamics, and we know how to treat those problems. But the problems of quantum critical phenomena in metals are unsettled problems. There are lot of fundamental things we don’t understand and I think we are starting to make progress on that. That is something I am very interested and excited in.
Right now, it looks like quantum computers are really on the horizon. Do you expect condensed matter physicists to contribute in a big way to this programme? What is your take?
Unfortunately, I am unconvinced that we are going to have a quantum computer in the near future. I hope we do, because we have promised society that we are going to produce one. And if we don’t produce one, we are going to look like liars. I do not know of any fundamental barrier to it. But I think on the whole, when physicists make claims about what’s practical, they are usually wrong. What’s practical turns on things beyond physics.
But for sure, if quantum computing is going to make progress, it is going to have a large contribution from condensed-matter physics. One of the most promising directions is using various sorts of superconducting qubits.
There are these ideas of topological quantum computing that come directly out of condensed-matter physics and are worked on by condensed-matter physicists. They are related to topologically ordered states and spin-liquid states.
So I think it’s very likely that if quantum computing becomes a reality, condensed-matter physics would will play a big role in that. My big worry is whether that is going to come to pass.
In conversations with Juan Maldacena, Nathan Seiberg and Abhay Ashtekar, it has come out that some new developments in theoretical high-energy physics could, in the near future, lead to the solutions for problems in strongly correlated electron systems. How do you see this development?
In the first place, the high-level statement is that theoretical physics is actually a unified subject. The methodologies, the way of thinking about things are certainly similar; the problems are very similar. The flow of information and ideas between [high-energy physics and condensed-matter physics] is exciting and important.
So what is unclear is the following: How many methods developed in quantum field theory or string theory will be imported to solve important problems in condensed-matter physics? That is not obvious.
What is obvious is that there are classes of highly correlated problems that have been solved using, for instance, the AdS/CFT correspondence.
[The AdS/CFT correspondence denotes a hypothetical connection between two kinds of theories in physics, of quantum gravity and of quantum field theories. It was first proposed by Juan Maldacena in 1997.]This has inspired us to think in new ways and to think of new possibilities. That has already happened and has had a major impact on our field.
- I am unconvinced that we are going to have a quantum computer in the near future.
So those are two separate problems. Whether there is going to be an important, identifiable problem in condensed-matter physics that we can just solve by applying some mathematical machinery [imported from theoretical high-energy physics] – that has happened in the past. It went both ways, with the renormalisation group ideas and quantum field theories being associated with critical points.
There was a flow of information back and forth between the statistical mechanics community and the quantum field theory community, which enriched both. That was actually one of the things that was going on when I was a postdoc in [the University of California, Santa Barbara]. There was this explosion of interest in common problems in field theory and statistical mechanics. That has already paid off in very big terms in both fields.
We are at an exciting time now, again, when both fields are talking to each other and exploring ways we can learn from each other. That is certainly good, but I do not think it has yet been proven that it gives a concrete solution to a specific problem.
Sounak Biswas and Prashant Kocherlakota are graduate students at the Tata Institute of Fundamental Research, Mumbai. Biswas is interested in various areas of condensed matter physics and statistical physics. Kocherlakota is a general relativist.