## Monday, October 07, 2019

### "Phase of matter" is a pretty amazing emergent concept

As we await the announcement of this year's physics Nobel tomorrow morning (last chance for predictions in the comments), a brief note:

I think it's worth taking a moment to appreciate just how amazing it is that matter has distinct thermodynamic phases or states.

We teach elementary school kids that there are solids, liquids, and gases, and those are easy to identify because they have manifestly different properties.  Once we know more about microscopic details that are hard to see with unaided senses, we realize that there are many more macroscopic states - different structural arrangements of solids; liquid crystals; magnetic states; charge ordered states; etc.

When we take statistical physics, we learn descriptively what happens.  When you get a large number of particles (say atoms for now) together, the macroscopic state that they take on in thermal equilibrium is the one that corresponds to the largest number of microscopic arrangements of the constituents under the given conditions.  So, the air in my office is a gas because, at 298 K and 101 kPa, there are many many more microscopic arrangements of the molecules with that temperature and pressure that look like a gas than there are microscopic arrangements of the molecules that correspond to a puddle of N2/O2 mixture on the floor.

Still, there is something special going on.  It's not obvious that there should have to be distinct phases at all, and such a small number of them.  There is real universality about solids - their rigidity, resistance to shear, high packing density of atoms - independent of details.  Likewise, liquids with their flow under shear, comparative incompressibility, and general lack of spatial structure.  Yes, there are detailed differences, but any kid can recognize that water, oil, and lava all have some shared "liquidity".  Why does matter end up in those configurations, and not end up being a homogeneous mush over huge ranges of pressure and temperature?  This is called emergence, because while it's technically true that the standard model of particle physics undergirds all of this, it is not obvious in the slightest how to deduce the properties of snowflakes, raindrops, or water vapor from there.    Like much of condensed matter physics, this stuff is remarkable (when you think about it), but so ubiquitous that it slides past everyone's notice pretty much of the time.

#### 1 comment:

Anonymous said...

I agree that phases of matter are often taken for granted without giving them the careful thought they deserve. A particularly fascinating aspect arises when we think of phases of matter, say a ferromagnet, from a quantum mechanical point of view. The linearity of QM allows for the ground state of such a many-particle system to be in a superposition of a state in which all the spins point up with a state in which all the spins point down. However, such a quantum superposition state is extremely sensitive to dephasing (as we take the number of spins to infinity) and collapses to a particular broken symmetry state (all spins up or all spins down). These broken symmetry states which we call as phases of matter are themselves fully quantum in nature, but largely immune to dephasing!

The situation is quite similar to SchrÃ¶dinger cat-like states which are superposition of coherent states and are extremely fragile. The coherent states themselves are robust against dephasing and are closest to approximation to a "classical" state. I wonder whether all phases of matter (quantum many-body ground states of interacting systems) are like coherent states which makes them robust against decoherence.

As decoherence is one of the biggest challenge in realising a quantum computer, shouldn't we work with "phases of matter" which are inherently protected against decoherence and yet have properties which can be exploited for quantum functionality? I suppose Kitaev's proposal based on exploiting topological excitations of a quantum many-body ground state is along these lines?