Criticality in the 2+1-dimensional compact Higgs model and fractionalized insulators

TL;DR

This paper introduces a new method to analyze critical behavior in a 2+1D compact Higgs model, revealing a resilient Z_2 universality class relevant to quantum phase transitions in fractionalized insulators.

Contribution

It develops a novel approach to compute critical exponents without hyperscaling, identifying a new universality class for quantum phase transitions in fractionalized insulators.

Findings

Alpha and nu vary along the critical line.

Resilience of Z_2 criticality observed.

Proposed universality class for insulator transition.

Abstract

We use a novel method of computing the third moment M_3 of the action of the 2+1-dimensional compact Higgs model in the adjoint representation with q=2 to extract correlation length and specific heat exponents nu and alpha, without invoking hyperscaling. Finite-size scaling analysis of M_3 yields the ratio (1+alpha)/nu and 1/nu separately. We find that alpha and nu vary along the critical line of the theory, which however exhibits a remarkable resilience of Z_2 criticality. We propose this novel universality class to be that of the quantum phase transition from a Mott-Hubbard insulator to a charge-fractionalized insulator in two spatial dimensions.