Optimal sampling of dynamical large deviations via matrix product states

TL;DR

This paper introduces an efficient sampling scheme for rare dynamical events in large deviation statistics using matrix product states, improving trajectory generation in complex lattice models.

Contribution

It develops a method leveraging MPS approximations of dominant eigenvectors to implement near-optimal sampling of rare events, extending tensor network techniques to trajectory sampling.

Findings

Successfully applied to Fredrickson-Andersen and East KCMs

Effective in symmetric simple exclusion process

Potential for extension to higher dimensions

Abstract

The large deviation (LD) statistics of dynamical observables is encoded in the spectral properties of deformed Markov generators. Recent works have shown that tensor network methods are well suited to compute the relevant leading eigenvalues and eigenvectors accurately. However, the efficient generation of the corresponding rare trajectories is a harder task. Here we show how to exploit the MPS approximation of the dominant eigenvector to implement an efficient sampling scheme which closely resembles the optimal (so-called "Doob") dynamics that realises the rare events. We demonstrate our approach on three well-studied lattice models, the Fredrickson-Andersen and East kinetically constrained models (KCMs), and the symmetric simple exclusion process (SSEP). We discuss how to generalise our approach to higher dimensions.