Stochastic strong zero modes and their dynamical manifestations

Klobas, Katja; Fendley, Paul; Garrahan, Juan P.

Abstract

Strong zero modes (SZMs) are conserved operators localized at the edges of certain quantum spin chains, which give rise to long coherence times of edge spins. Here we define and analyze analogous operators in one-dimensional classical stochastic systems. For concreteness, we focus on chains with single occupancy and nearest-neighbor transitions, in particular particle hopping and pair creation and annihilation. For integrable choices of parameters we find the exact form of the SZM operators. Being in general nondiagonal in the classical basis, the dynamical consequences of stochastic SZMs are very different from those of their quantum counterparts. We show that the presence of a stochastic SZM is manifested through a class of exact relations between time-correlation functions, absent in the same system with periodic boundaries.

Citation

Klobas, K., Fendley, P., & Garrahan, J. P. (2023). Stochastic strong zero modes and their dynamical manifestations. Physical Review E, 107(4), Article L042104. https://doi.org/10.1103/PhysRevE.107.L042104

• Journal Article Type: Article
• Acceptance Date: Apr 6, 2023
• Online Publication Date: Apr 28, 2023
• Publication Date: Apr 28, 2023
• Deposit Date: May 19, 2023
• Publicly Available Date: May 19, 2023
• Journal: Physical Review E
• Print ISSN: 1539-3755
• Electronic ISSN: 2470-0053
• Publisher: American Physical Society
• Peer Reviewed: Peer Reviewed
• Volume: 107
• Issue: 4
• Article Number: L042104
• DOI: https://doi.org/10.1103/PhysRevE.107.L042104
• Keywords: Classical mechanics; Classical statistical mechanics; Lattice dynamics; Nonequilibrium statistical mechanics; Stochastic processes; 1-dimensional spin chains; 1-dimensional systems; Exclusion processes; Lattice models in statistical physics; Nonequilibrium lattice models; Nonequilibrium systems; Many-body techniques; Monte Carlo methods
• Public URL: https://nottingham-repository.worktribe.com/output/20555161
• Publisher URL: https://journals.aps.org/pre/abstract/10.1103/PhysRevE.107.L042104
• Additional Information: 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.