Effective Field Theory and Integrability in Two-Dimensional Mott Transition

TL;DR

This paper explores the Mott transition in a 2D lattice model, revealing its topological nature through effective field theory and integrability, and identifying a quantum group symmetry at criticality.

Contribution

It derives a lattice double Chern-Simons theory as the effective field theory and uncovers the topological and symmetry properties of the Mott transition in the model.

Findings

The Mott transition is topological with vortex and d-density wave order.

The effective field theory is a lattice double Chern-Simons theory with k=1.

Weak coupling leads to a quantum gas-liquid transition in the Ising universality class.

Abstract

We study the Mott transition in a two-dimensional lattice spinless fermion model with nearest neighbors density-density interactions. By means of a two-dimensional Jordan-Wigner transformation, the model is mapped onto the lattice XXZ spin model, which is shown to possess a Quantum Group symmetry as a consequence of a recently found solution of the Zamolodchikov Tetrahedron Equation. A projection (from three to two space-time dimensions) property of the solution is used to identify the symmetry of the model at the Mott critical point as U_q(sl(2))xU_q(sl(2)), with deformation parameter q=-1. Based on this result, the low-energy Effective Field theory for the model is obtained and shown to be a lattice double Chern-Simons theory with coupling constant k=1 (with the standard normalization). By further employing the Effective Filed Theory methods, we show that the Mott transition that arises is of topological nature, with vortices in an antiferromagnetic array and matter currents characterized by a d-density wave order parameter. We also analyze the behavior of the system upon weak coupling, and conclude that it undergoes a quantum gas-liquid transition which belongs to the Ising universality class.