Designer Monte Carlo simulation for the Gross-Neveu-Yukawa transition

Abstract

In this paper, we study the quantum criticality of Dirac fermions via large-scale numerical simulations, focusing on the Gross-Neveu-Yukawa chiral-Ising quantum critical point (QCP) with critical bosonic modes coupled with Dirac fermions. We show that finite-size effects at this QCP 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 a nonlocal update of the bosonic field, we find that moderately large system size (up to 16×16) is already sufficient to produce robust scaling behavior and critical exponents. The conductance of free 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.