Tag Archives: condensed matter

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.

Congratulations to Thouless, Haldane, and Kosterlitz!

I’m traveling this week in sunny California, so I don’t have time for a long post, but I thought I should mention that the 2016 Nobel Prize in Physics has been announced. Instead of going to LIGO, as many had expected, it went to David Thouless, Duncan Haldane, and Michael Kosterlitz. LIGO will have to wait for next year.

Thouless, Haldane, and Kosterlitz are condensed matter theorists. While particle physics studies the world at the smallest scales and astrophysics at the largest, condensed matter physics lives in between, explaining the properties of materials on an everyday scale. This can involve inventing new materials, or unusual states of matter, with superconductors being probably the most well-known to the public. Condensed matter gets a lot less press than particle physics, but it’s a much bigger field: overall, the majority of physicists study something under the condensed matter umbrella.

This year’s Nobel isn’t for a single discovery. Rather, it’s for methods developed over the years that introduced topology into condensed matter physics.

Topology often gets described in terms of coffee cups and donuts. In topology, two shapes are the same if you can smoothly change one into another, so a coffee cup and a donut are really the same shape.

mug_and_torus_morphMost explanations stop there, which makes it hard to see how topology could be useful for physics. The missing part is that topology studies not just which shapes can smoothly change into each other, but which things, in general, can change smoothly into each other.

That’s important, because in physics most changes are smooth. If two things can’t change smoothly into each other, something special needs to happen to bridge the gap between them.

There are a lot of different sorts of implications this can have. Topology means that some materials can be described by a number that’s conserved no matter what (smooth) changes occur, leading to experiments that see specific “levels” rather than a continuous range of outcomes. It means that certain physical setups can’t change smoothly into other ones, which protects those setups from changing: an idea people are investigating in the quest to build a quantum computer, where extremely delicate quantum states can be disrupted by even the slightest change.

Overall, topology has been enormously important in physics, and Thouless, Haldane, and Kosterlitz deserve a significant chunk of the credit for bringing it into the spotlight.