Concentrated Monte Carlo sampling for local observables in quantum spin chains

TL;DR

This paper introduces a concentrated Monte Carlo sampling method that improves the efficiency and accuracy of estimating local observables in short-range correlated quantum spin systems by focusing on the surroundings of the observable.

Contribution

The paper proposes a novel concentrated Monte Carlo sampling approach that enhances local observable estimation in quantum spin chains with short-range correlations.

Findings

Higher accuracy for local observables in short-range correlated states

Requires fewer samples compared to conventional methods

Effective in both ground and thermal states of quantum spin models

Abstract

Monte Carlo methods are widely used to estimate observables in many-body quantum systems. However, conventional sampling schemes often require a large number of samples to achieve sufficient accuracy. In this work we propose the concentrated Monte Carlo sampling approach, which builds on the idea that in systems with only short range correlations, to obtain accurate expectation values for local observables, one would favor detailed information in the surroundings of this observable compared to far away from it. In this approach we consider all possible configurations in the surroundings of a local observable, and unique samples from the remaining of the setup drawn using Markov chain Monte Carlo. We have tested the performance of this approach for ground states of the spin-1/2 tilted Ising model in different phases, and also for thermal states in the a spin-1 bilinear-biquadratic model. Our results demonstrate that CMCS yields higher accuracy for local observables in short-range correlated states while requiring substantially fewer samples, showcasing in which regimes one can obtain acceleration for the evaluation of expectation values.