It is hard to overstate the impact that Anderson had on the field. In terms of pure scientific results, there are others far more skilled than I who can describe his contributions, but I will mention a few that are well known:
- He developed what is now known as the Anderson model, a theoretical treatment originally intended to capture the essential physics in some transition metal-based magnets. The model considers comparatively localized d orbitals and includes both hopping to neighboring sites in a lattice as well as the "on-site repulsion" U that makes it energetically expensive to have two electrons (in a spin singlet) on the same site. This leads to "superexchange" processes, where energetically costly double-occupancy is a virtual intermediate state. The Anderson model became the basis for many developments - allow coupling between the local sites and delocalized s or p bands, and you get the Kondo model. Put in coupling to lattice vibrations and you get the Anderson-Holstein model. Have a lattice and make the on-site repulsion really strong, and you get the Hubbard model famed in correlated electron circles and as the favored treatment of the copper oxide superconductors.
- Anderson also made defining contributions to the theory of localization. Electrons in solids are wavelike, and in perfect crystal lattices the ones in the conduction and valence bands propagate right past the ions because the waves themselves account for the periodicity of the lattice. Anderson showed that even in the absence of interactions (the electron-electron repulsion), disorder can scatter those waves, and interference effects can lead to situations where the final result is waves that are exponentially damped with distance. This is called Anderson localization, and it applies to light and sound as well as electrons. With strict conditions, this result implies that (ignoring interactions) infinitesimal amounts of disorder can make a 2D electronic system an insulator.
- Here is his Nobel Lecture, by the way, that really focuses on these two topics.
- In considering superconductivity, Anderson also discovered what is now known as the Higgs mechanism, showing that while the bare excitations of some quantum field theory could be massless, coupling those excitations to some scalar field whose particular value broke an underlying symmetry could lead to an effective mass term (in the sense of how momentum and energy relate to each other) for the originally massless degrees of freedom. Since Anderson himself wrote about this within the last five years, I have nothing to add.
- Anderson also worked on superfluidity in 3He, advancing understanding of this first-discovered non-electronic paired superfluid and its funky properties due to p-wave pairing.
- With the discovery of the copper oxide superconductors, Anderson introduced the resonating valence bond (RVB) model that still shapes discussions of these and exotic spin-liquid systems.
Anderson was unquestionably a brilliant person who in many ways defined the modern field of condensed matter physics. He was intellectually active right up to the end, and he will be missed. (For one of my own interactions with him, see here.)
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Beautiful sentiments, Doug. There are countless contributions that Phil Anderson made to physics, of course. You did a great job highlighting most of them, but I'd like to add another (and other posters will certainly have more) that, arguably, was his most broad-ranging and influential work, perhaps even moreso than the Higgs.
I am talking about his development with Sir Sam Edwards of the "replica" theory of spin glasses, as exemplified by the Edwards-Anderson Hamiltonian, and the corresponding application of the replica method and mean field theory to its analysis with Thouless and Palmer. This work laid the foundation for a more complete solution to the spin glass problem by Toulouse and Parisi, and the ideas and concepts from spin glasses that emerged have found application in areas as diverse as neural networks / deep learning, protein folding, evolution, and countless other disciplines well beyond the realm of 'traditional' physics.
However, despite being such a great physicist, I think I will most remember Phil for his graciousness and generosity.
I had the good fortune of meeting Phil once in my life. I was a second-year graduate student helping to organize a student-run conference for condensed matter physics, and we decided to invite Phil. I remember how nerve-wracking it was introducing P.W. Anderson to a room of condensed matter physicists - I felt like a college basketball player introducing Michael Jordan. In fact, I said exactly that in my introduction, and in response, Phil smiled, laughed and said "Nice introduction!" that made me feel more confident in myself.
At dinner afterwards, I got the chance to talk to him personally some more. I was still very young, and in the early, difficult stages of graduate school, where I was coming to grips with just how little physics I really knew. I was still trying to figure out how to 'do' research. I told Phil about the confusion I was having in not knowing exactly how I should be approaching my problem, and asked him if it was normal to just feel like you were 'winging it' sometimes. He was so down-to-earth and easy going, and answered my questions in a casual, friendly tone, without being arrogant or condescending at all.
Phil must have had tens of thousands of interactions with people from all walks of life, and I doubt he remembered me much, if at all. But to me, it was one of the biggest highlights of my career. Phil Anderson was my hero, and I had always been told 'never meet your heroes', since they would inevitably fall short of expectations. But I was lucky enough that my hero was one of the few that didn't.
Nice story, PPP. The other piece of physics I thought about including was what is now known as the Anderson orthogonality catastrophe, which I'd mentioned here.
My other PWA anecdote: During "dead week" senior year of undergrad (between the end of classes and the start of finals), some of the graduating physics majors decided to have a cookout on the Jadwin loading dock, with beer, at the end of the day on (I believe) a Friday. PWA drives up and parks his car, some big old steel behemoth, behind the building and comes up via the loading dock to get inside. He looked at us curiously for a second, then realized what was going on, gave a little half-smile and kept walking. I offered him a beer, and he very politely said, "No, thank you" and went into the building. For someone who could be prickly, he seemed pretty amused.
There are a bunch of other seminal Anderson contributions:
1.Anderson-Halperin-Varma TLS model of low temperature glasses.
2."Kubo" theory of stochastic line shapes prior to Kubo (Anderson's PhD thesis).
3.Theory of double exchange and superexchange.
4.Seminal contributions to scaling and RG via "poor man's" scaling approach to Kondo model (Anderson-Yuval-Hamann).
5.Anderson's theorem describing protection of s-wave superconductivity against disorder.
I'm sure there are others...
David, yes, and there are more. As I have been reminded via email by others:
6. The pseudogap (with relevance to spin and charge density waves, with Lee and Rice, Solid State Communications, 14(8), 703-709 (1974)).
7. Motional narrowing of spectral lines (Journal of the Physical Society of Japan, 9(3), 316-339 (1954)).
8. The original spin liquid/resonating valence bond paper (Materials Research Bulletin, 8(2), 153-160. (1973)).
9. Starquakes, glitches in neutron stars, and superfluidity of degenerate neutron matter (Nature, 256(5512), 25-27 (1975)).
The Anderson/Halperin/Varma model of two-level systems in glasses was the major basis for my doctoral thesis, and I should have linked to this post about it.
And my link broke. I meant http://nanoscale.blogspot.com/2009/10/unreasonable-effectiveness-of-toy-model.html.
Hi Doug-absolutely. Actually your point (7) is what I meant by my (2).
One last thing-about the TLS picture. After 5 decades finally computer simulation is up to the task of testing the picture-see: https://arxiv.org/abs/1910.11168 ...also discussed (a little bit) here:
https://www.quantamagazine.org/ideal-glass-would-explain-why-glass-exists-at-all-20200311/
Speaking of high-temperature superconductivity, this new approach made possible by COVID-19 seems promising: https://arxiv.org/abs/2003.14321
Phil would be proud...maybe
Thank you for the nice post. I should add two other seminal contributions from PWA:
* The very early work at Bell on the microscopic origin of the ferroelectric transition in perovskites done under Shockley
(the papers have been reprinted in "A career in theoretical physics").
* The work with E. I. Blount (Phys. Rev. Lett. 14, 217 (1965)) where they predicted that ferroelectric-like transitions can in principle occur in metals. This was observed in LiOsO3 a few years ago and has given rise to the very active field of a polar-metals.
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