I'm an experimentalist who is mainly focusing on strongly correlated electron systems (SCES), in particular Metal-insulator (Mott) transitions in the classical example $V_2 O_3$. Recently I decided to gain some more insight into the theoretical aspects of these SCES, e.g. field theoretical approaches. I started reading some lecture notes from https://www.cond-mat.de/events/correl17/manuscripts/correl17.pdf where I was " suprised" by a statement that was made on p.I.23. They state that the Luttinger theorem is not violated by the behavior of Mott insulators because the transition is observed for relatively high temperatures. However, a little bit further in section 6, they suggest that if a Mott insulator could exist at zero temperature it would have some topological/quantum order (see also footnote)?

Does someone has an idea about how these Mott insulators are currently conceived in the recent revolution of quantum/topological order, or can someone comment on the statements made in this paragraph to clarify what is meant? Literature related to these statements are also welcome! Thank you!

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    $\begingroup$ (1/2)That first chapter is a nice, if maybe a little idiosyncratic, overview of some aspects of strongly-correlated systems. I won't hazard a full answer to this problem, but I think in all known cases an unordered Mott insulator at high temperature eventually develops some order as temperature is lowered. For example, in the $d>=2$ Hubbard model, it might develop antiferromagnetic order (remaining an insulator) or superconducting order (becoming a conductor), depending on filling. $\endgroup$ – Rococo Nov 16 '19 at 16:59
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    $\begingroup$ (2/2) So, the author is presenting some interesting speculation about whether this is a strict requirement or whether the unordered Mott insulator can persist all the way down to T=0, in which case it would be some sort of exotic spin-liquid insulator. However, this might be a quite unusual condition, and it does not appear that the author has a specific model which is proposed to exhibit this ground state. $\endgroup$ – Rococo Nov 16 '19 at 16:59
  • $\begingroup$ You might consider taking a look at the textbook "Quantum Phase Transitions" by Subir Sachdev, if you haven't already. $\endgroup$ – aquirdturtle Nov 17 '19 at 5:26
  • $\begingroup$ Recent papers have cast doubt on $V_2 O_3$ being a purely Mott insulator. See this paper, for instance. $\endgroup$ – wyphan Dec 5 '20 at 0:06

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