Variational Monte Carlo (VMC) with row-update Projected Entangled-Pair States (PEPS) and its applications in quantum spin glasses

TL;DR

This paper introduces an autoregressive row-update sampling method for PEPS in VMC, significantly improving convergence and stability in simulating quantum spin systems, especially near critical points and in frustrated landscapes.

Contribution

It proposes a novel autoregressive row-wise sampling algorithm for PEPS-VMC that reduces correlations and enhances efficiency in quantum many-body simulations.

Findings

Mitigates critical slowing down near phase transitions.

Achieves lower ground-state energies in quantum spin glasses.

Improves sampling efficiency over traditional local updates.

Abstract

Solving the quantum many-body ground state problem remains a central challenge in computational physics. In this context, the Variational Monte Carlo (VMC) framework based on Projected Entangled Pair States (PEPS) has witnessed rapid development, establishing itself as a vital approach for investigating strongly correlated two-dimensional systems. However, standard PEPS-VMC algorithms predominantly rely on sequential local updates. This conventional approach often suffers from slow convergence and critical slowing down, particularly in the vicinity of phase transitions or within frustrated landscapes. To address these limitations, we propose an efficient autoregressive row-wise sampling algorithm for PEPS that enables direct, rejection-free sampling via single-layer contractions. By utilizing autoregressive single-layer row updates to generate collective, non-local configuration proposals, our method significantly reduces temporal correlations compared to local Metropolis moves. We benchmark the algorithm on the two-dimensional transverse-field Ising model and the quantum spin glass. Our results demonstrate that the row-wise scheme effectively mitigates critical slowing down near the Ising critical point. Furthermore, in the rugged landscape of the quantum spin glass, it yields improved optimization stability and lower ground-state energies. These findings indicate that single-layer autoregressive row updates provide a flexible and robust improvement to local PEPS-VMC sampling and may serve as a basis for more advanced sampling schemes.