Exact Monte Carlo time dynamics in many-body lattice quantum systems

TL;DR

This paper extends an exact Monte Carlo algorithm based on Feynman-Kac formulas to simulate time-dependent correlations in many-body lattice quantum systems, with rigorous fluctuation control and practical examples.

Contribution

It introduces a method for exact simulation of time-dependent correlations in lattice quantum systems, adapting and proving the validity of fluctuation control techniques.

Findings

Successful extension to time-dependent correlation functions

Rigorous proof of fluctuation control methods

Practical examples with Hubbard and Heisenberg models

Abstract

On the base of a Feynman-Kac--type formula involving Poisson stochastic processes, recently a Monte Carlo algorithm has been introduced, which describes exactly the real- or imaginary-time evolution of many-body lattice quantum systems. We extend this algorithm to the exact simulation of time-dependent correlation functions. The techniques generally employed in Monte Carlo simulations to control fluctuations, namely reconfigurations and importance sampling, are adapted to the present algorithm and their validity is rigorously proved. We complete the analysis by several examples for the hard-core boson Hubbard model and for the Heisenberg model.