Spencer Stirling's Research Interests
Spencer Stirling

MY BACKGROUND: theoretical physics, mathematics (sometimes called "mathematical physics")

Introduction to quantum PHASES: because cold materials are weird
I study exotic states of matter (called "quantum phases") that form when materials are very cold (near absolute zero).

When a material is "cold" the particles inside are sluggish and do not move/vibrate/bump into one another very much. The colder it gets, the more unlikely it is for a particle to be energetic. In fact, this is what the word "temperature" means to physicists: it is a statistical measure that describes how likely it is for a particle to be in random motion (for interested people, I recommend taking an undergraduate statistical mechanics courses).

19th century physics told us that the particles would stop moving completely if we could cool them enough (this extreme situation only exists in our minds - it could NEVER actually be achieved in the laboratory). This unreachable limit is called "absolute zero temperature". However, when we add in 20th century ideas about quantum mechanics, even at absolute zero particles can be "kicked around" and bump into one another (NOTE: it often happens in science that a description of nature will break down when we apply it to extreme circumstances. This does NOT mean that 19th century statistical mechanics is wrong. Absolute zero is simply beyond its range of validity, and people already SUSPECTED that long before quantum mechanics).

This strange behavior arises because of the Heisenberg uncertainty principle (Delta E Delta t >= hbar), which tells us that the energy can, and WILL, fluctuate for very short periods of time. This won't affect heavy particles much (because they have a lot of inertia and it takes a lot of energy to "get them moving"), but lighter particles are easily perturbed by these quantum fluctuations. At higher temperatures these quantum fluctuations are "drowned out" by thermal fluctuations (so we don't see them), but near absolute zero we can see how the quantum world by itself behaves. Hence, even at absolute zero some materials can have very interesting properties (without quantum fluctuations + lightweight particles the material would be very boring because nothing moves).

How do materials behave near absolute zero? First, we all know that materials are made of atoms (which, of course, are just electrons orbiting around a heavy nucleus). However, a material should NOT be thought of as simply a "bunch of atoms". Instead, when many atoms are packed closely together (as in a solid) then the electrons are free to float from atom to atom (rather than simply orbiting around their home nucleus). Hence a solid actually appears like a bunch of stationary atomic nuclei surrounded by a SEA of electrons.

How can quantum energy fluctuations affect the sea of electrons? The answer is more complicated than we might think at first. It turns out that even a SINGLE electron is too heavy to be kicked around (much) by quantum fluctuations. In most materials this is enough to make things very boring. On the other hand, in very special materials the situation is just right so that electrons can easily move collectively. For example, imagine waves forming in the sea of electrons. Although the random energy from the Heisenberg uncertain principle is not enough to kick around even a single electron much, it IS enough to excite these "collective excitations".

This seems counterintuitive: if the energy is not enough to kick around even a single electron, how can it kick around MANY cooperating electrons? Actually, we have a lot of experience with this kind of phenomena in everyday life. Imagine a boat hitched to the back of a truck. Nobody is strong enough to more either the boat or the truck (at least not much). However, when they are hitched together, even a child can continuosly jump up and down on the back of the boat and set up a pattern of vibrations that shakes the truck TOGETHER with the boat quite vigorously.

The "waves in the electron sea" is a useful analogy, but actually it's not really right. Since we're not being exactly precise anyway, let us switch to another useful analogy: a WHIRLPOOL in the sea of electrons. Notice that we have not even mentioned the atomic nuclei because they are far too heavy to be affected by quantum fluctuations.

The trouble (and the interesting part) comes when we try to mathematically model the cooperative behavior in the sea of electrons. It is impossible to track the motion of each electron separately (in principle we know how to do this, but in practice it's far too complicated). Instead, it's much easier (and more enlightening) to "zoom out" and ignore the detailed motion of the individual electrons. We want to limit our thoughts to the collective motions (the whirlpools). We can treat the whirlpools as "fake particles" that can interact with other "fake particles" (whirlpools), and disregard the underlying details. Also, from our zoomed-out perspective, the electron sea is just a stage where the actors (the fake particles) perform.

We call the whirlpools (the fake particles) "quasiparticles" because we know that they are not fundamental particles (at a more detailed level they are actually collective motions of electrons), but we don't need to know those details in order to model how whirlpools move and interact with each other. Also, using an analogy with fundamental particle physics (where the "actors" (electrons, protons, etc) perform in the vacuum of space), we may be tempted to call the sea of electrons a "material vacuum" (this is a strange sort of vacuum indeed). Together, the quasiparticles and the material vacuum are called "emergent" phenomena because they emerge from the more fundamental electron behavior. The underlying electrons are said to be "strongly-correlated" because they cooperate strongly.

Side remarks: deeper implications for physics?
If we think about the discussion above, we have some emergent physics from some more fundamental physics. If we pause for a second to think about the usual "fundamental particles" in physics (electrons, quarks, etc), we might speculate that they also may not actually be fundamental, either. They also might be "emergent" quasiparticles from even MORE fundamental particles that have not yet been discovered. Hence this research (which started by thinking about materials) may have deep implications in particle physics as well.

Topological phases: a special (and useful!) class of quantum phases
I mostly work with a special class of quantum phases that are called "topological phases". In topological phases the quasiparticles all behave as though they have MASS (i.e. they have inertia). These behave very differently from the massLESS quasiparticles that are seen in other quantum phases (comparing with particle physics, we know that MASSIVE electrons behave very differently from MASSLESS light).

To understand the difference we need to think about energy. We all know that any type of particle has kinetic energy when it MOVES through the vacuum (the same applies to fake quasiparticles travelling through the fake material vacuum). The important point is that there is no limitation on how small the kinetic energy can be. On the other hand, massive particles have ANOTHER type of "locked up" energy. This is because Einstein said that mass is basically another form of energy E=mc^2. This means that particles from a "massive species" require a minimum amount of energy E=mc^2 even to exist! By contrast, massLESS particles (like light in particle physics) can form from arbitrarily-small amounts of energy (and all that energy goes into movement).

Because of this, we say that massive particles are "gapped" (there is a fixed energy cost to create a particle, even one that is stationary), whereas massLESS particles are "gapless" (any amount of energy will create one). If we REALLY want to abuse our whirlpool example, a "massive" type of whirlpool is a whirlpool species that only comes in a fixed size, and no smaller! (It is not obvious what whirlpool SIZE has to do with its MASS. Let me explain: a whirlpool costs energy to create because it is, after all, made up of a bunch of swirling electrons. Bigger whirlpools obviously have more internal energy. We can view this internal energy as the cost of existence, i.e. "mass".)

Massive quasiparticles may not seem strange (after all, in particle physics almost ALL particles have mass). However, it is important to remember that in particle physics there is one notable massless type of particle: LIGHT. The existence of light changes the entire physics of the universe, and hence fundamental particle physics behaves somewhat UNLIKE the topological phases in materials that we are discussing (however, if we could somehow "ban" massless light from existence, then our universe would behave very differently. It would be in a topological phase).

Although it is not obvious, the absence of massless quasiparticles has a strange effect on topological phases: instead of having a unique material vacuum, there are actually MANY material vacuums (the underlying sea of electrons can be in one of many different lowest-energy configurations). Let's call it the material "multi-vacuum". In technical jargon, physicists say that a topological phase has many "degenerate ground states". This type of behavior is quite exotic because it does not appear in particle physics (imagine if there were many different types of "vacuum of space"). Even more strangely, for some reason the number of material vacuums depends on the approximate shape of the material (more precisely, the topology)!

Topological phases may be technological basis for powerful new "quantum" computer
One exciting application of topological phases is that INFORMATION can be safely stored in this material multi-vacuum, and it can ONLY be accessed and modified by manipulating quasiparticles. Since the quasiparticles have mass, it is relatively easy to avoid creating them accidentally (because it takes a fixed amount of energy to create them). Hence the information is protected from corruption. This is definitely different from storing information in regular materials (where massless particles (e.g. light and phonons=sound waves) are often created accidentally, striking the data-storage particles and corrupting them).

This by itself would not be a great achievement (we already have computers and harddrives to store and process information, and we have other methods to counteract data corruption). However, the "information" that I am discussing is not the ordinary computer "bits" that we are used to. Instead it is information with some bizarre quantum qualities ("qbits"). Qbits have ENTANGLEMENT properties that seem rather magical (it is NOT magic, just physics). If we can control qbits then we can build a "quantum computer" with capabilities far beyond ordinary computers (note: by "ordinary computers" I mean everything ranging from the simple abacus all the way up to futuristic supercomputers).

Toy models of topological phases
Unfortunately, there are many obstacles to overcome because we still know so little about topological phases. Up to now I have mostly been studying and creating mathematical models of "toy" topological phases (i.e. models that may not actually exist in nature, but teach us a lot about how topological phases work). However, these days I am interested in moving my efforts toward real materials (which usually requires physical modelling on the computer).

Deep connections in pure mathematics
Originally I became involved in this type of physics by studying some closely-related topics in mathematics during my PhD (I have always split my time equally between physics and mathematics). These mathematical topics have names like topological quantum field theory (TQFT), category theory (ribbon/modular tensor categories), Chern-Simons, and conformal field theory (CFT). It appears that we need these new mathematical ideas in order to provide an effective description for the emergent physics (strange new physics requires strange new mathematics). Sadly the mathematics has developed somewhat independently of the physics, and the cultures remain fairly separated even now. If you are considering a career in this field then I recommend you study EITHER pure condensed matter physics OR the pure mathematical areas. Unfortunately the two cultures (and hence FUNDING agencies) have not embraced the interdisciplinary area (although I still believe this is the future, and this is where I remain until I leave the field altogether because I cannot feed my family).

My advisor was Prof. Dan Freed in the Geometry Group at the University of Texas at Austin.

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