Zero-temperature Monte Carlo simulations of two-dimensional quantum spin glasses guided by neural network states

TL;DR

This paper employs neural network-guided quantum Monte Carlo simulations to study the ground state and phase transition of a two-dimensional quantum spin glass, providing new insights into its critical properties and overlap distribution.

Contribution

It introduces neural network-guided Monte Carlo methods to accurately simulate large quantum spin glasses and estimate their critical parameters.

Findings

Neural network guiding reduces population control bias effectively.

Finite-size scaling estimates the critical transverse field and exponents consistent with literature.

Spin-overlap distribution shows a non-trivial double-peak shape within the spin-glass phase.

Abstract

A continuous-time projection quantum Monte Carlo algorithm is employed to simulate the ground state of a short-range quantum spin-glass model, namely, the two-dimensional Edwards-Anderson Hamiltonian with transverse field, featuring Gaussian nearest-neighbor couplings. We numerically demonstrate that guiding wave functions based on self-learned neural networks suppress the population control bias below modest statistical uncertainties, at least up to a hundred spins. By projecting a two-fold replicated Hamiltonian, the spin overlap is determined. A finite-size scaling analysis is performed to estimate the critical transverse field where the spin-glass transition occurs, as well as the critical exponents of the correlation length and the spin-glass susceptibility. For the latter two, good agreement is found with recent estimates from the literature for different random couplings. We also address the spin-overlap distribution within the spin-glass phase, finding that, for the workable system sizes, it displays a non-trivial double-peak shape with large weight at zero overlap.