Topological phases in the dynamics of the simple exclusion process

TL;DR

This paper explores how the symmetric simple exclusion process exhibits distinct topological phases in its rare dynamical trajectories, revealing new topological phenomena in classical stochastic systems through advanced tensor network methods.

Contribution

It introduces the identification of symmetry protected topological phases in the dynamical large deviations of the SSEP using tensor network techniques and eigenstate analysis.

Findings

Identification of trivial and non-trivial SPT phases at half-filling.

Existence of phase transitions between different SPT phases.

Manifestation of topological phases in rare stochastic trajectories.

Abstract

We study the dynamical large deviations of the classical stochastic symmetric simple exclusion process (SSEP) by means of numerical matrix product states. We show that for half-filling, long-time trajectories with a large enough imbalance between the number hops in even and odd bonds of the lattice belong to distinct symmetry protected topological (SPT) phases. Using tensor network techniques, we obtain the large deviation (LD) phase diagram in terms of counting fields conjugate to the dynamical activity and the total hop imbalance. We show the existence of high activity trivial and non-trivial SPT phases (classified according to string-order parameters) separated by either a critical phase or a critical point. Using the leading eigenstate of the tilted generator, obtained from infinite-system density matrix renormalisation group (DMRG) simulations, we construct a near-optimal dynamics for sampling the LDs, and show that the SPT phases manifest at the level of rare stochastic trajectories. We also show how to extend these results to other filling fractions, and discuss generalizations to asymmetric SEPs.