Monte Carlo methods in continuous time for lattice Hamiltonians

TL;DR

This paper introduces continuous-time quantum Monte Carlo methods for lattice Hamiltonian models, effectively addressing sign problems in lattice field theories and enabling new non-perturbative analysis approaches.

Contribution

It presents novel continuous-time Monte Carlo techniques utilizing dual representations to solve sign problems in lattice Hamiltonian models.

Findings

Successfully solves sign problems in Yukawa and gauge theories

Develops quantum Monte Carlo methods for non-perturbative dynamics

Provides a new computational framework for lattice field theories

Abstract

We solve a variety of sign problems for models in lattice field theory using the Hamiltonian formulation, including Yukawa models and simple lattice gauge theories. The solutions emerge naturally in continuous time and use the dual representation for the bosonic fields. These solutions allow us to construct quantum Monte Carlo methods for these problems. The methods could provide an alternative approach to understanding non-perturbative dynamics of some lattice field theories.