Monte Carlo simulation of boson lattices

TL;DR

This paper introduces two advanced Monte Carlo methods, SSE with directed loops and CTDMC, for simulating boson lattices described by the Hubbard model, demonstrating their effectiveness on a 1D spin-1 boson system.

Contribution

It presents two novel Monte Carlo approaches, SSE with directed loops and CTDMC, for improved simulation of boson lattice models, especially in avoiding discretization errors and handling ground states.

Findings

Evidence for a dimerized ground state in the lowest Mott lobe

Effective simulation of anti-ferromagnetic spin-1 bosons in 1D

Advancement in computational methods for lattice models

Abstract

Boson lattices are theoretically well described by the Hubbard model. The basic model and its variants can be effectively simulated using Monte Carlo techniques. We describe two newly developed approaches, the Stochastic Series Expansion (SSE) with directed loop updates and continuous--time Diffusion Monte Carlo (CTDMC). SSE is a formulation of the finite temperature partition function as a stochastic sampling over product terms. Directed loops is a general framework to implement this stochastic sampling in a non--local fashion while maintaining detailed balance. CTDMC is well suited to finding exact ground--state properties, applicable to any lattice model not suffering from the sign problem; for a lattice model the evolution of the wave function can be performed in continuous time without any time discretization error. Both the directed loop algorithm and the CTDMC are important recent advances in development of computational methods. Here we present results for a Hubbard model for anti--ferromagnetic spin--1 bosons in one dimensions, and show evidence for a dimerized ground state in the lowest Mott lobe.