Monday, December 30, 2013

Links and thanks at the end of another year

Thank you, readers, for another year.  It is gratifying to hear from you and to meet people who have found this blog useful and informative (or at least worth noticing, which is something these days).  My posting frequency slumped quite a bit at the end of 2013 because of various writing commitments (a couple of which continue).  I'm hoping to have some more to say in the coming year, and I hope that there are opportunities out there to get some of the coolness of condensed matter and nanoscale physics to the general public as well as my more specialized readers.

Here are a few end-of-year links for your enjoyment:
  • Sometimes people put amusing or snarky comments in the acknowledgments sections of papers.  Who knew?  (Full disclosure:  It's possible that the "M. Fleetwood" acknowledged in this paper is a musician.)
  • Scientists and mathematicians have their own special brand of humor.  (I love the Mandelbrot joke.  This does omit one of my favorites:  What is purple and commutes?  An Abelian grape.)
  • Bob Laughlin is jumping back into physics aiming to make a big splash:  He basically is arguing (see this preprint) that there really is no such thing as a Mott insulator.  That's a rather radical statement at this point, given (for example) experiments with optical lattices that seem to show that the Mott insulator appears to exist as a realizable state.  (I'm sure there are ways to argue that those experiments are not really in the thermodynamic limit and involve interactions that are not the Coulomb interaction, etc.)
  • Snowflakes are still cool.  (A repeat, but worth it.)


David Brown said...

Why not give us a list of great unsolved problems in condensed matter physics?

Peter Armitage said...

Hi Doug,

Personally I believe that Mott insulators exist, but I don't believe a proof has come from the atom experiments. The Mott effect definitely exist (Bob presumably agrees on this point) e.g. strong local interactions suppress mobility and create a gap-like structure in D(E). But the issue is whether or not the mobility becomes zero for some finite (e.g. non-infinite) interaction strength. The atom experiments didn't show this. All they show is there is a transition from a superfluid state, to a non-sf state with very local correlations. They don't show that its mobility is zero (or even "small"...). And although they show a gap structure in the excitation spectra, they can't show (I don't believe), that it is a clean gap.

Other people are much more experts than me, but I think it could be argued that even DMFT hasn't shown a Mott insulator exists, because the finite size effects haven't been explored in detail. Its clear from DMFT that crossovers exist that look like a Mott transition, but whether the low energy spectral weight just getting very small or is really going to zero is unknown.

Its hard to separate out disorder effects in charge transport experiments on presumptive (magnetic order free) Mott insulators. Materials like the quantum spice ices and herbertsmithite are chock-full of disorder than conceivably could localize bands already made narrow by interactions.

Despite all this, I still think Mott insulators exists though! Experimental (or numerical proof) is hard though.

Douglas Natelson said...

Hi Peter, I am on the same page as you on this topic. Having read Bob's paper, his point of view is quite interesting and thought-provoking (as always). Starting from a noninteracting system at T=0, imagine dialing up the interactions. Bob says that there's nothing crazy about the idea that you could cross a quantum phase transition to a localized state. However, he clearly thinks that has not been demonstrated theoretically, particularly in the sense of writing down an actual trial wavefunction on the insulating side in terms of the coordinates of the electrons that really minimizes the energy and shows a gap. Not surprising that Bob thinks a lot in terms of wave functions, given what he did in the FQHE case.

It's interesting, as you pointed out several years ago here, that conceptually the Mott insulator is the easiest kind of insulator to explain to a kid, and yet it's so hard to nail down theoretically. I'd be curious for some theorist response to Bob's points....

Ted Sanders said...
This comment has been removed by the author.
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