The Many Worlds of Condensed Matter

Physics is the science of the very big and the very small. We study the smallest scales, the fundamental particles that make up the universe, and the largest, stars on up to the universe as a whole.

We also study the world in between, though.

That’s the domain of condensed matter, the study of solids, liquids, and other medium-sized arrangements of stuff. And while it doesn’t make the news as often, it’s arguably the biggest field in physics today.

(In case you’d like some numbers, the American Physical Society has divisions dedicated to different sub-fields. Condensed Matter Physics is almost twice the size of the next biggest division, Particles & Fields. Add in other sub-fields that focus on medium-sized-stuff, like those who work on solid state physics, optics, or biophysics, and you get a majority of physicists focused on the middle of the distance scale.)

When I started grad school, I didn’t pay much attention to condensed matter and related fields. Beyond the courses in quantum field theory and string theory, my “breadth” courses were on astrophysics and particle physics. But over and over again, from people in every sub-field, I kept hearing the same recommendation:

“You should take Solid State Physics. It’s a really great course!”

At the time, I never understood why. It was only later, once I had some research under my belt, that I realized:

Condensed matter uses quantum field theory!

The same basic framework, describing the world in terms of rippling quantum fields, doesn’t just work for fundamental particles. It also works for materials. Rather than describing the material in terms of its fundamental parts, condensed matter physicists “zoom out” and talk about overall properties, like sound waves and electric currents, treating them as if they were the particles of quantum field theory.

This tends to confuse the heck out of journalists. Not used to covering condensed matter (and sometimes egged on by hype from the physicists), they mix up the metaphorical particles of these systems with the sort of particles made by the LHC, with predictably dumb results.

Once you get past the clumsy journalism, though, this kind of analogy has a lot of value.

Occasionally, you’ll see an article about string theory providing useful tools for condensed matter. This happens, but it’s less widespread than some of the articles make it out to be: condensed matter is a huge and varied field, and string theory applications tend to be of interest to only a small piece of it.

It doesn’t get talked about much, but the dominant trend is actually in the other direction: increasingly, string theorists need to have at least a basic background in condensed matter.

String theory’s curse/triumph is that it can give rise not just to one quantum field theory, but many: a vast array of different worlds obtained by twisting extra dimensions in different ways. Particle physicists tend to study a fairly small range of such theories, looking for worlds close enough to ours that they still fit the evidence.

Condensed matter, in contrast, creates its own worlds. Pick the right material, take the right slice, and you get quantum field theories of almost any sort you like. While you can’t go to higher dimensions than our usual four, you can certainly look at lower ones, at the behavior of currents on a sheet of metal or atoms arranged in a line. This has led some condensed matter theorists to examine a wide range of quantum field theories with one strange behavior or another, theories that wouldn’t have occurred to particle physicists but that, in many cases, are part of the cornucopia of theories you can get out of string theory.

So if you want to explore the many worlds of string theory, the many worlds of condensed matter offer a useful guide. Increasingly, tools from that community, like integrability and tensor networks, are migrating over to ours.

It’s gotten to the point where I genuinely regret ignoring condensed matter in grad school. Parts of it are ubiquitous enough, and useful enough, that some of it is an expected part of a string theorist’s background. The many worlds of condensed matter, as it turned out, were well worth a look.

9 thoughts on “The Many Worlds of Condensed Matter

  1. physicsphile

    I’d like to try and self study condensed matter. I have done a course in quantum field theory. Do you have any text book recommendations?


      1. shomiller

        The solid state class here at Stony Brook didn’t have a real textbook the last few years, but the best book we were referred to was “Condensed Matter Field Theory”, by Altland and Simons. It doesn’t assume QFT and tries to teach it throughout from the condensed matter point of view, but it does so through a series of important applications. It also has a lot of great problems and includes descriptions of the solutions that can be really helpful for self-studying.

        I’ve also heard good things about Phillip Phillips’ book, “Advanced Solid State Physics”, but I haven’t read much of that one myself.


  2. Xezlec

    Ugh… in the engineering program at my university, we had to take a course called “Solid State Electronic Devices”, which purported to teach us how things like transistors work and how to engineer them at the materials level to have desired properties. It was awful. They tried to teach us (undergrads with no prior QM, mind you) quantum mechanics in the first couple weeks, then solid state physics and the specific details of different devices. They went as far as electron bandstructure in 3 dimensions…

    I guess they were hoping to get us interested, but instead I came out of that class certain in the knowledge that I could never understand physics and could hope for nothing more than to be useful to the kind of people who can.

    Currently I work at a lab that does a bunch of research in environmental acoustics. Which category does that fall into in your list of fields? Fluid dynamics, maybe?


    1. 4gravitonsandagradstudent Post author

      Probably yeah, though I get the impression acoustics is sort of a weird interdisciplinary field rather than a physics subfield in practice.

      Your solid state class indeed sounds pretty awful, it does seem like the sort of thing that’s hard to appreciate if you don’t have the right background.


  3. Machine Learning

    I’ve a couple of question, the first serious, the second a joke…

    Do you think that the usage of quantum field theory in condensed matter can help to to dive into the issue of decoherence (and the quantum->classical transition)?

    When you read about tensor network (which reminds me tensor flow and big data) ” In 1997, Juan Maldacena found a concrete example of holography in action, demonstrating that a toy model describing a flat space without gravity is equivalent to a description of a saddle-shaped space with gravity” or “the holographic concept to a two-dimensional computer chip that contains the code for creating the three-dimensional virtual world of a video game. We live within that 3-D game space. In one sense, our space is illusory, an ephemeral image projected into thin air.” don’t you find any worrying similarities with the ridiculous flat earth myth?? lol lol


    1. 4gravitonsandagradstudent Post author

      The impression I have is that it’s harder to see decoherence-like phenomena in quantum field theory than in quantum mechanics, and that this is part of what makes it hard to formalize the connection between entanglement/complexity and space-time that a lot of holography people are interested in. But I may be mixing up two unrelated problems.

      Clearly the flat earth people were talking about holography all along, we should have known! 😉

      Liked by 1 person

  4. Peter

    This post is great! I have always been fascinated by the intersection of condensed matter and high energy physics. In addition to things like Ads/CFT correspondence and the holographic description of superconductivity etc, do you know any more interesting connections between the two fields and specifically more advanced field theoretic tools shared by them in common? Do you think a (theoretical) condensed matter student interested in this intersection can have a chance to work on high energy/string related projects for careers after phd?(the opposite way might be easy?) What should be prepared for that?


    1. 4gravitonsandagradstudent Post author

      From what I’ve seen, there are two broad classes of situations where CMT and HET share important field theoretic tools: field theories on boundaries, and renormalization group flows. Both of those are areas where I’ve seen a lot of collaboration between CMT and HET people, and in particular a lot of HET people referencing CMT work.

      It’s definitely possible to start out in CMT and collaborate on HET/string work during your postdoc. Different places have different amounts of this sort of collaboration: here at Perimeter there’s a lot of cross-talk between people in the string theory and condensed matter groups, for example. If you’re aiming for that sort of thing, I’d mostly advise focusing on the more field-theoretic aspects of condensed matter (and as mentioned, boundaries and RG), and to look around and see what people are collaborating on where you are.



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