Optimal sampling of dynamical large deviations in two dimensions via tensor networks

TL;DR

This paper employs tensor network methods to analyze large deviation statistics and phase transitions in two-dimensional dynamical models, providing a new computational approach for studying rare events and phase behavior.

Contribution

It introduces a PEPS-based framework for calculating large deviations and sampling rare trajectories in 2D dynamical systems, revealing phase transition characteristics.

Findings

First-order phase transition in 2D East model.

Indications of second-order transition in 2D SSEP.

PEPS enables direct sampling of rare trajectories.

Abstract

We use projected entangled-pair states (PEPS) to calculate the large deviations (LD) statistics of the dynamical activity of the two dimensional East model, and the two dimensional symmetric simple exclusion process (SSEP) with open boundaries, in lattices of up to 40x40 sites. We show that at long-times both models have phase transitions between active and inactive dynamical phases. For the 2D East model we find that this trajectory transition is of the first-order, while for the SSEP we find indications of a second order transition. We then show how the PEPS can be used to implement a trajectory sampling scheme capable of directly accessing rare trajectories. We also discuss how the methods described here can be extended to study rare events at finite times.