The Stochastic Green Function (SGF) algorithm

TL;DR

The paper introduces the Stochastic Green Function (SGF) algorithm, a versatile quantum Monte Carlo method for simulating bosonic systems on lattices in continuous time, offering exact results and access to Green functions.

Contribution

The SGF algorithm is a novel, dimension-independent quantum Monte Carlo method that efficiently simulates multi-species bosonic Hamiltonians in continuous imaginary time.

Findings

Works in any dimension without discretization errors

Handles multiple boson species and Bose-Fermi systems

Provides access to n-body Green functions

Abstract

We present the Stochastic Green Function (SGF) algorithm designed for bosons on lattices. This new quantum Monte Carlo algorithm is independent of the dimension of the system, works in continuous imaginary time, and is exact (no error beyond statistical errors). Hamiltonians with several species of bosons (and one-dimensional Bose-Fermi Hamiltonians) can be easily simulated. Some important features of the algorithm are that it works in the canonical ensemble and gives access to n-body Green functions.