Addressing general measurements in quantum Monte Carlo

TL;DR

This paper introduces a universal scheme in quantum Monte Carlo to address the sign problem and measurement issues by expressing observables as ratios of partition functions, enabling broader application in quantum many-body systems.

Contribution

The authors propose a novel reweight-annealing scheme that separates and estimates partition functions for general measurements, applicable to various models and correlation types.

Findings

Successfully applied to XXZ and transverse field Ising models

Handles multi-body and non-local correlations

Works for space and time reweighting

Abstract

Quantum Monte Carlo is one of the most promising approaches for dealing with large-scale quantum many-body systems. It has played an extremely important role in understanding strongly correlated physics. However, two fundamental problems, namely the sign problem and general measurement issues, have seriously hampered its scope of application. We propose a universal scheme to tackle the problems of general measurement. The target observables are expressed as the ratio of two types of partition functions $\langle \mathrm{O} \rangle=\bar{Z}/Z$, where $\bar{Z}=\mathrm{tr} (\mathrm{Oe^{-\beta H}})$ and $Z=\mathrm{tr} (\mathrm{e^{-\beta H}})$. These two partition functions can be estimated separately within the reweight-annealing frame, and then be connected by an easily solvable reference point. We have successfully applied this scheme to XXZ model and transverse field Ising model, from 1D to 2D systems, from two-body to multi-body correlations and even non-local disorder operators, and from equal-time to imaginary-time correlations. The reweighting path is not limited to physical parameters, but also works for space and time. Essentially, this scheme solves the long-standing problem of calculating the overlap between different distribution functions in mathematical statistics, which can be widely used in statistical problems, such as quantum many-body computation, big data and machine learning.