Topological phases in the dynamics of the simple exclusion process

Garrahan, Juan P.; Pollmann, Frank

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.

Citation

Garrahan, J. P., & Pollmann, F. (2024). Topological phases in the dynamics of the simple exclusion process. Physical Review E, 109(3), Article L032105. https://doi.org/10.1103/PhysRevE.109.L032105

• Journal Article Type: Article
• Acceptance Date: Feb 14, 2024
• Online Publication Date: Mar 11, 2024
• Publication Date: 2024-03
• Deposit Date: Feb 14, 2024
• Publicly Available Date: Feb 14, 2024
• Journal: Physical Review E
• Print ISSN: 2470-0045
• Electronic ISSN: 2470-0053
• Publisher: American Physical Society
• Peer Reviewed: Peer Reviewed
• Volume: 109
• Issue: 3
• Article Number: L032105
• DOI: https://doi.org/10.1103/PhysRevE.109.L032105
• Keywords: Symmetry protected topological states; Exclusion processes; Large deviation & rare event statistics
• Public URL: https://nottingham-repository.worktribe.com/output/31443961
• Publisher URL: https://journals.aps.org/pre/abstract/10.1103/PhysRevE.109.L032105