A Unified Framework for Cluster Methods with Tensor Networks

TL;DR

This paper introduces a unified tensor network framework for cluster MCMC methods, enabling flexible and efficient sampling in many-body systems, and demonstrates its application to classical spin models.

Contribution

It develops a general tensor-based cluster MCMC framework that unifies existing algorithms and extends their capabilities for complex many-body simulations.

Findings

Unified tensor network cluster MCMC framework

Applied to 2D Edwards-Anderson and 3D Ising models

Enables arbitrary cluster updates using TNs

Abstract

Markov Chain Monte Carlo (MCMC), and Tensor Networks (TN) are two powerful frameworks for numerically investigating many-body systems, each offering distinct advantages. MCMC, with its flexibility and theoretical consistency, is well-suited for simulating arbitrary systems by sampling. TN, on the other hand, provides a powerful tensor-based language for capturing the entanglement properties intrinsic to many-body systems, offering a universal representation of these systems. In this work, we leverage the computational strengths of TN to design a versatile cluster MCMC sampler. Specifically, we propose a general framework for constructing tensor-based cluster MCMC methods, enabling arbitrary cluster updates by utilizing TNs to compute the distributions required in the MCMC sampler. Our framework unifies several existing cluster algorithms as special cases and allows for natural extensions. We demonstrate our method by applying it to the simulation of the two-dimensional Edwards-Anderson Model and the three-dimensional Ising Model. This work is dedicated to the memory of Prof. David Draper.