## Wednesday, September 04, 2019

### Big questions about condensed matter (part 2)

Continuing, another question asked by Ross McKenzie's son:

2. Scientific knowledge changes with time. Sometimes long-accepted facts''  and theories'' become overturned? What ideas and results are you presenting that you are almost absolutely certain of? What might be overturned?

I think this question is framed interestingly.  Physics in general and condensed matter in particular is a discipline where the overturning of long-accepted ideas has often really meant a clearer appreciation and articulation about the limits of validity of models, rather than a wholesale revision of understanding.

For example, the Mermin-Wagner theorem is often mentioned as showing that one cannot have true two-dimensional crystals (this would be a breaking of continuous translational symmetry).  However, the existence of graphene and other atomically thin systems like transition metal dichalcogenides, and the existence of magnetic order in some of those materials, are experimentally demonstrated.  That doesn't mean that Mermin-Wagner is mathematically incorrect.  It means that one must be very careful in defining what is meant by "truly two-dimensional".

There are many things in condensed matter that are as "absolutely certain" as anything gets in science.  The wave nature of x-rays, electrons, and neutrons plus the spatial periodicity of matter in crystals leads to clear diffraction patterns.  That same spatial periodicity strongly influences the electronic properties of crystals (Bloch's theorem, labeling of states by some wavevector-like parameter $\mathbf{k}$, some energy dependence of those states $E(\mathbf{k})$).   More broadly, there are phases of matter that can be classified by symmetries and topology, with distinct macroscopic properties.  The macroscopic phases that are seen in equilibrium are those that correspond to the largest number of microscopic configurations subject to any overall constraints (that's the statistical physics basis for thermodynamics).  Amazingly, knowing the ground state electronic density of a system everywhere means its possible in principle to calculate just about everything about the ground state.

Leaving those aside, asking what might be overturned is a bit like asking where we might find either surprises or mistakes in the literature.  Sometimes seemingly established wisdom does get upset.  One recent example:  For a couple of decades, it's been thought that Sr2RuO4 is likely a spin-triplet superconductor, where the electron pairs are p-wave paired (have net orbital angular momentum), and is an electronic analog to the A phase of  superfluid 3He.  Recent results suggest that this is not correct, and that the early evidence for this is not seen in new measurements.   There are probably more things like this out there, but it's hard to speculate.  Bear in mind, though, that science is supposed to work like this.  In the long run, the truth will out.

Peter Morgan said...

QM can be understood as a Koopman-Hilbert space formalism for CM (Classical Mechanics, not Condensed Matter.) All the Hilbert space math stays the same, so not a big deal, but claims that QM is qualitatively different from CM will come to seem significantly overblown, and I suppose some journalists will hammer down hard on that aspect. I believe an attitude such as you express above, that there both is change and is not, will be essential.
The fundamental principle IMO is that noncommutative measurements are rather obviously classically natural from a signal analysis perspective, because fourier analysis is heavily used, whereas only commutative measurements have seemed natural from the perspective of Hamiltonian/Lagrangian/other formalisms for CM. Nonlocality is present in this construction, but it is adequately constrained by the requirement for Lorentz invariance, so not too big a deal.
End of cryptically terse comment! Obviously I have to persuade people of the above, which, given that others have pursued the same mathematics and failed, I may well not be able to do. See arXiv:1901.00526, if you will, which is not perfect but has been with Annals of Physics for review for the last two months: you'll be unsurprised to hear that a few people on social media find this compelling but many people do not.

Muntasir R Mahdi said...

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I appreciated the writing and the information you've given here.
Thank you again.

Muntasir Mahdi

Diego Pasquier said...

Hi, thanks for the nice post, the example of Sr2RuO4 is interesting indeed. Do you believe that some conventional wisdom about the cuprate superconductors might also change? (see e.g. https://physics.aps.org/articles/v10/129)