# Using matrix product states to study the dynamical large deviations of kinetically constrained models

## TL;DR

This paper applies tensor network techniques, specifically matrix product states, to analyze rare event statistics and dynamical phase transitions in kinetically constrained models relevant to glasses, enabling detailed finite-size scaling studies.

## Contribution

It introduces a novel application of tensor network methods to kinetically constrained models, allowing high-accuracy approximation of eigenstates related to large deviation statistics.

## Key findings

- Successfully characterizes finite size scaling of dynamical phase transitions.
- Analyzes spectral gaps and spatial structure of dynamical phases.
- Demonstrates tensor networks' effectiveness in studying large systems.

## Abstract

Here we demonstrate that tensor network techniques - originally devised for the analysis of quantum many-body problems - are well suited for the detailed study of rare event statistics in kinetically constrained models (KCMs). As concrete examples we consider the Fredrickson-Andersen and East models, two paradigmatic KCMs relevant to the modelling of glasses. We show how variational matrix product states allow to numerically approximate - systematically and with high accuracy - the leading eigenstates of the tilted dynamical generators which encode the large deviation statistics of the dynamics. Via this approach we can study system sizes beyond what is possible with other methods, allowing us to characterise in detail the finite size scaling of the trajectory-space phase transition of these models, the behaviour of spectral gaps, and the spatial structure and "entanglement" properties of dynamical phases. We discuss the broader implications of our results.