Directed Loop Updates for Quantum Lattice Models

TL;DR

This paper extends the quantum Monte Carlo directed loop update technique to various quantum lattice models, providing efficient algorithms for complex systems like spin, boson, and fermion models.

Contribution

It introduces a generalized approach for applying directed loop updates to a broad class of quantum lattice models, enhancing simulation efficiency.

Findings

Efficient 'no-bounce' algorithms identified for specific parameter regimes.

Applicable to Spin-S XXZ, boson, and 1D spinful fermion models.

Provides explicit expressions for optimal parameter regimes.

Abstract

This article outlines how the quantum Monte Carlo directed loop update recently introduced can be applied to a wide class of quantum lattice models. Several models are considered: Spin-S XXZ models with longitudinal and transverse magnetic fields, boson models with two-body interactions, and 1D spinful fermion models. Expressions are given for the parameter regimes were very efficient "no-bounce" quantum Monte Carlo algorithms can be found.