Effective field theory and integrability in two-dimensional Mott transition

Abstract

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 dimen- sions) property of the solution is used to identify the symmetry of the model at the Mott critical point as Uq([sl(2)) ⊗ Uq([sl(2)), with deformation param- eter 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 transi- tion 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.