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!