# Metal-insulator transition a quantum phase transition?

One can consider two main types of metal-insulator transitions (MIT), nl. interaction-driven (Mott) or disorder-driven (Anderson-Mott). Recently, I have been reading that these MIT might also have quantum phase transition features (e.g. see https://arxiv.org/pdf/cond-mat/0309604.pdf p.30). However, the explanation remains rather vague in this reference.

Could someone provide me with a better explanation on how the metal-insulator transitions might be a quantum phase transitions, e.g. what are the arguments to suspect this? Good references (beside Sachdev's book) are also welcome! Thank you in advance.

I think that the Mott transition is an example of a quantum phase transition in the sense that it is not temperature dependent but one that happens at $$T=0$$ as a parameter of the system is tuned. Looking at the Hubbard model at half-filling, for example, then it is clear that for $$U\to\infty$$ the system is insulating (all states are singly occupied and no hopping is allowed) while for $$U=0$$ the system is conducting. The study of this quantum phase transition is still ongoing, to the best of my knowledge. You can read about one the methods used to study it in this review(?) by Prof. Kotliar using the dynamical mean field theory. In Fig 1.1 (page 11 in the link) you can see how, as $$U$$ is increased, the conduction band splits into two bands with a finite gap between them. This is the Mott transition.
• Yes sure I'm familiar with the DMFT approach of the Mott transition, and ok, the Mott transition has a non-thermal order/control parameter but that doesn't necessarily mean it will be a quantum phase transition?? For example, what about quantum critical behavior of the Mott transition? How does this transition behave at $T=0$ because often it has been studied at finite $T$. – Simon Feb 18 '20 at 18:43
• @Simon A phase transition at $T=0$ is a quantum phase transition by definition. – Seth Whitsitt Feb 18 '20 at 20:37
• @Simon as I said, the study of this transition is ongoing, to the best of my knowledge. However, the argument that the ground states of $U\to\infty$ and of $U=0$ belong to different phases (insulator vs. conductor) is enough to convince that there is a phase-transition at $T=0$, no? (unless you're worried that one of these phases is realized only at the extreme point, which I think is easy to see is not the case) – user245141 Feb 19 '20 at 9:27