Mott transition and integrable lattice models in two dimensions

TL;DR

This paper explores a two-dimensional Mott transition in a Hubbard-like model, revealing a topological phase transition characterized by vortices and duality, with implications for quantum phases and experimental observations.

Contribution

It introduces an integrable two-dimensional lattice model based on the Zamolodchikov tetrahedron equation, linking topological order with Mott transition phenomena.

Findings

Mott transition occurs in a d-density wave or staggered flux phase.

Transition characterized by vortices and electric-magnetic duality.

Doping leads to a quantum gas-liquid coexistence phase in the Ising universality class.

Abstract

We describe the two-dimensional Mott transition in a Hubbard-like model with nearest neighbors interactions based on a recent solution to the Zamolodchikov tetrahedron equation, which extends the notion of integrability to two-dimensional lattice systems. At the Mott transition, we find that the system is in a d-density wave or staggered flux phase that can be described by a double Chern Simons effective theory with symmetry \su2 \otimes \su2. The Mott transition is of topological nature, characterized by the emergence of vortices in antiferromagnetic arrays interacting strongly with the electric charges and an electric-magnetic duality. We also consider the effect of small doping on this theory and show that it leads to a quantum gas-liquid coexistence phase, which belongs to the Ising universality class and which is consistent with several experimental observations.