Thermal Ising transitions in the vicinity of two-dimensional quantum critical points

TL;DR

This paper uses quantum Monte Carlo simulations to study the scaling behavior of thermal Ising transitions near quantum critical points in two-dimensional systems, providing insights into universal properties and critical exponents.

Contribution

It offers detailed numerical analysis of the scaling relations and critical exponents near quantum critical points in 2D systems, including new estimates for the chiral Ising transition.

Findings

Confirmed scaling predictions for the quantum Ising model with high precision.

Extracted critical exponents for the chiral Ising transition consistent with recent estimates.

Provided numerical evidence for universal behavior near quantum critical points.

Abstract

The scaling of the transition temperature into an ordered phase close to a quantum critical point as well as the order parameter fluctuations inside the quantum critical region provide valuable information about universal properties of the underlying quantum critical point. Here, we employ quantum Monte Carlo simulations to examine these relations in detail for two-dimensional quantum systems that exhibit a finite-temperature Ising-transition line in the vicinity of a quantum critical point that belongs to the universality class of either (i) the three-dimensional Ising model for the case of the quantum Ising model in a transverse magnetic field on the square lattice or (ii) the ${\it chiral}$ Ising transition for the case of a half-filled system of spinless fermions on the honeycomb lattice with nearest-neighbor repulsion. While the first case allows large-scale simulations to assess the scaling predictions to a high precision in terms of the known values for the critical exponents at the quantum critical point, for the later case we extract values of the critical exponents $\nu$ and $\eta$, related to the order parameter fluctuations, which we discuss in relation to other recent estimates from ground state quantum Monte Carlo calculations as well as analytical approaches.