Direct sampling of projected entangled-pair states

TL;DR

This paper introduces a new direct sampling algorithm for PEPS that produces independent samples, improving the efficiency of variational Monte Carlo methods for 2D quantum models.

Contribution

It generalizes an existing direct sampling method to PEPS, enabling independent sampling and more accurate expectation value evaluation.

Findings

The algorithm reduces autocorrelation issues in PEPS sampling.

Benchmark results show improved sampling efficiency on classical and quantum models.

Demonstrates potential for enhanced variational Monte Carlo studies.

Abstract

Variational Monte Carlo studies employing projected entangled-pair states (PEPS) have recently shown that they can provide answers on long-standing questions such as the nature of the phases in the two-dimensional $J_1 - J_2$ model. The sampling in these Monte Carlo algorithms is typically performed with Markov Chain Monte Carlo algorithms employing local update rules, which often suffer from long autocorrelation times and interdependent samples. We propose a sampling algorithm that generates independent samples from a PEPS, bypassing all problems related to finite autocorrelation times. This algorithm is a generalization of an existing direct sampling algorithm for unitary tensor networks. We introduce an auxiliary probability distribution from which independent samples can be drawn, and combine it with importance sampling in order to evaluate expectation values accurately. We benchmark our algorithm on the classical Ising model and on variational optimization of two-dimensional quantum spin models.