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  • Letter
  • Open Access

Topological phases in the dynamics of the simple exclusion process

Juan P. Garrahan1,2 and Frank Pollmann3,4

  • 1School of Physics and Astronomy, University of Nottingham, Nottingham NG7 2RD, United Kingdom
  • 2Centre for the Mathematics and Theoretical Physics of Quantum Non-Equilibrium Systems, University of Nottingham, Nottingham NG7 2RD, United Kingdom
  • 3Department of Physics and Institute for Advanced Study, Technical University of Munich, D-85748 Garching, Germany
  • 4Munich Center for Quantum Science and Technology (MCQST), Schellingstrasse 4, D-80799 München, Germany

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Phys. Rev. E 109, L032105 – Published 11 March, 2024

DOI: https://doi.org/10.1103/PhysRevE.109.L032105

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 nontrivial 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 renormalization group 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.

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Phys. Rev. E 109, L032105– Published 11 March, 2024
  • Received 5 February 2024
  • Accepted 13 February 2024
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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