I just completed my first draft of Chapter 8: Topology Matters for Condensed Matter Physics: A Very Short Introduction.
Any comments and suggestions would be appreciated. I learned a lot writing the chapter, but imagine it needs to be made more accessible.
Very interesting! I'm in physics, but not condensed matter, so this is basically new to me. I have a few comments:
ReplyDelete"Only change in steps" in the first sentence is unclear to me. I assume it's meant like "number of holes changes only in discrete steps, so topology cares about it, but smooth deformation can be broken down into infinitesimal pieces, so topology disregards those differences", but at first it read to me as if smooth deformations *were* what you meant by steps - i.e. they are changes that happen step by step, rather than all at once. I feel like just saying topology only cares about qualities that are preserved by smooth changes, like stretching and bending.
I also think saying "for a ball, donut, and... pretzel, these... are one, two, and three" might be unclear for someone new to the field who doesn't realize you're referring to a *hollowed out* donut (torus), since an actual physical edible donut only has one hole. Similarly with "holes" in a baseball vs a basketball.
It might also be nice to a have a picture labeling the holes, since the "donut hole" is sort of qualitatively different from the "interior chamber" of the torus, and it might not be clear to a lay person "what we count as holes".
I haven't actually read chapter 4, but the second paragraph does seem pretty technical. A picture might help, depending on how often these concepts have been brought up previously in the book.
I think a picture of "holes" (positive charge carriers, not topological holes) hopping around would also be helpful.
I wasn't able to get through all the rest, but it seemed reasonably clear (again, as a non CM physicist). But more pictures might be helpful in general.
Thanks for the comments and feedback. It is extremely helpful.
DeleteVery nice!
ReplyDeleteJust a comment/question: the ground state of 1D AFM has gapless excitations for half-odd integer spins, whereas that for integer spins is separated from all excited states by a finite spin gap (Haldane gap).
In both cases there is no long-range order in agreement with Wigner-Mermin theorem.
Isn't his correct that for integer spins correlation decays exponentially and for half-integer it decaying as a power law? Then, half-integer spins do not exhibit infinite range correlation.