Designer Monte Carlo Simulation for Gross-Neveu Transition

TL;DR

This paper introduces a model design and simulation approach for studying the Gross-Neveu-Yukawa quantum critical point with Dirac fermions, achieving accurate critical exponents and conductance behavior through large-scale quantum Monte Carlo simulations.

Contribution

It presents a novel model design that minimizes finite-size effects and combines it with an efficient self-learning quantum Monte Carlo algorithm for studying fermionic quantum critical points.

Findings

Finite-size effects can be minimized via model design.

Moderately-large system sizes suffice for robust scaling.

Conductance behavior matches conformal field theory predictions.

Abstract

In this manuscript, we study quantum criticality of Dirac fermions via large-scale numerical simulations, focusing on the Gross-Neveu-Yukawa(GNY) chiral-Ising quantum critical point with critical bosonic modes coupled with Dirac fermions. We show that finite-size effects at this quantum critical point can be efficiently minimized via model design, which maximizes the ultraviolet cutoff and at the same time places the bare control parameters closer to the nontrivial fixed point to better expose the critical region. Combined with the efficient self-learning quantum Monte Carlo algorithm, which enables non-local update of the bosonic field, we find that moderately-large system size (up to $16\times 16$) is already sufficient to produce robust scaling behavior and critical exponents.The conductance of the Dirac fermions is also calculated and its frequency dependence is found to be consistent with the scaling behavior predicted by the conformal field theory. The methods and model-design principles developed for this study can be generalized to other fermionic QCPs, and thus provide a promising direction for controlled studies of strongly-correlated itinerant systems.