Multi-discontinuity algorithm for world-line Monte Carlo simulations

TL;DR

The paper presents a new multi-discontinuity Monte Carlo algorithm that improves the efficiency of simulating quantum systems, especially for studying Bose-Einstein condensates of composite particles, by overcoming previous limitations.

Contribution

A novel multi-discontinuity algorithm generalizing previous methods, enabling efficient simulation of complex quantum systems and BEC of composite particles.

Findings

Solves the freezing problem in simulations of S=1 antiferromagnets with strong anisotropy.

Enables efficient computation of off-diagonal correlators for composite particle BEC.

Demonstrates effectiveness through simulations of a specific Hamiltonian.

Abstract

We introduce a novel multi-discontinuity algorithm for efficient global update of world-line configurations in Monte Carlo simulations of interacting quantum systems. This new algorithm is a generalization of the two-discontinuity algorithms introduced in Refs. [N. Prokof'ev, B. Svistunov, and I. Tupitsyn, Phys. Lett. A {\bf 238}, 253 (1998)] and [O. Sylju{\aa}sen and A. Sandvik, Phys. Rev. E {\bf 66}, 046701 (2002)] . This generalization is particularly effective for studying Bose-Einstein condensates (BEC) of composite particles. In particular, we demonstrate the utility of the generalized algorithm by simulating a Hamiltonian for an S=1 anti-ferromagnet with strong uniaxial single-ion anisotropy. The multi-discontinuity algorithm not only solves the freezing problem that arises in this limit, but also allows for efficiently computing the off-diagonal correlator that characterizes a BEC of composite particles.