Exact, Complete, and Universal Continuous-Time Worldline Monte Carlo Approach to the Statistics of Discrete Quantum Systems

TL;DR

This paper introduces an exact continuous-time worldline quantum Monte Carlo method for discrete quantum systems, eliminating discretization errors and enabling efficient calculation of various physical quantities.

Contribution

It formulates a continuous-time worldline Monte Carlo approach that is exact, free of small parameters, and applicable to arbitrary discrete quantum systems.

Findings

The method is exact and free of discretization errors.

It allows efficient updates via worldline discontinuities.

It can compute dynamic correlations and work with grand canonical ensemble.

Abstract

We show how the worldline quantum Monte Carlo procedure, which usually relies on an artificial time discretization, can be formulated directly in continuous time, rendering the scheme exact. For an arbitrary system with discrete Hilbert space, none of the configuration update procedures contain small parameters. We find that the most effective update strategy involves the motion of worldline discontinuities (both in space and time), i.e., the evaluation of the Green's function. Being based on local updates only, our method nevertheless allows one to work with the grand canonical ensemble and non-zero winding numbers, and to calculate any dynamic correlation function as easily as expectation values of, e.g., total energy. The principles found for the update in continuous time generalize to any continuous variables in the space of discrete virtual transitions, and in principle also make it possible to simulate continuous systems exactly.