Gross-Neveu Heisenberg criticality: dynamical generation of quantum spin Hall masses

TL;DR

This paper investigates the quantum phase transition in a honeycomb lattice fermion model that exhibits Gross-Neveu Heisenberg criticality, using quantum Monte Carlo simulations to precisely compute critical exponents and susceptibilities.

Contribution

It provides high-precision numerical results for critical exponents and susceptibilities in a lattice model demonstrating Gross-Neveu Heisenberg criticality, highlighting the importance of susceptibilities in large-N limits.

Findings

Critical exponents for N=3: 1/ν=1.11(4), η_φ=0.80(9), η_ψ=0.29(2)

Susceptibilities are crucial for analyzing large-N Gross-Neveu transitions

Demonstrates dynamical generation of quantum spin Hall masses in a lattice model

Abstract

We consider fermions on a honeycomb lattice supplemented by a spin invariant interaction that dynamically generates a quantum spin Hall insulator. This lattice model provides an instance of Gross-Neveu Heisenberg criticality, as realized for example by the Hubbard model on the honeycomb lattice. Using auxiliary field quantum Monte Carlo simulations we show that we can compute with unprecedented precision susceptibilities of the order parameter. In O(N) Gross-Neveu transitions, the anomalous dimension of the bosonic mode grows as a function of N such that in the large-N limit it is of particular importance to consider susceptibilities rather than equal time correlations so as to minimize contributions from the background. For the N=3 case, we obtain $1/\nu=1.11(4)$, $\eta_{\phi}=0.80(9)$, and $\eta_{\psi}=0.29(2)$ for respectively the correlation length exponent, bosonic and fermionic anomalous dimensions.