$Z_2$-gauge theory description of the Mott transition in infinite dimensions

TL;DR

This paper maps the infinite dimensional Hubbard model onto a $Z_2$ gauge-invariant fermion-spin model, revealing the Mott transition as a spontaneous $Z_2$ gauge symmetry breaking, and solves it exactly using dynamical mean-field theory.

Contribution

It introduces a novel $Z_2$ gauge theory framework for the Mott transition in infinite dimensions and provides an exact solution via dynamical mean-field theory.

Findings

Mott transition corresponds to spontaneous $Z_2$ gauge symmetry breaking.

Exact solution of the spin-fermion model at zero and finite temperature.

Identification of an order parameter for the Mott transition.

Abstract

The infinite dimensional half-filled Hubbard model can be mapped exactly with no additional constraint onto a model of free fermions coupled in a $Z_2$ gauge-invariant manner to auxiliary Ising spins in a transverse field. In this slave-spin representation, the zero-temperature insulator-to-metal transition translates into spontaneous breaking of the local $Z_2$ gauge symmetry, which is not forbidden in infinite dimensions, thus endowing the Mott transition of an order parameter that is otherwise elusive in the original fermion representation. We demonstrate this interesting scenario by exactly solving the effective spin-fermion model by dynamical mean-field theory both at zero and at finite temperature.