Stochastic strong zero modes and their dynamical manifestations
arXiv:2205.09110 · doi:10.1103/PhysRevE.107.L042104
Abstract
Strong zero modes (SZMs) are conserved operators localised at the edges of certain quantum spin chains, which give rise to long coherence times of edge spins. Here we define and analyse analogous operators in one-dimensional classical stochastic systems. For concreteness, we focus on chains with single occupancy and nearest-neighbour 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 non-diagonal 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.
arXiv comment5+8 pages, 4 figures; v2 published version
References in corpus (26)
- Unpaired Majorana fermions in quantum wires
- Many body localization and thermalization in quantum statistical mechanics
- From Quantum Chaos and Eigenstate Thermalization to Statistical Mechanics and Thermodynamics
- Quantum many-body systems out of equilibrium
- Nonequilibrium Steady States of Matrix Product Form: A Solver's Guide
- Quantum Many-Body Scars and Hilbert Space Fragmentation: A Review of Exact Results
- Recent progress in many-body localization
- Quasilocal charges in integrable lattice systems
- Parafermionic edge zero modes in Z_n-invariant spin chains
- Topological phases with parafermions: theory and blueprints
- Representations of the quadratic Algebra and Partially Asymmetric Diffusion with Open Boundaries
- Partially Asymmetric Exclusion Process with Open Boundaries
- Exact Spectral Gaps of the Asymmetric Exclusion Process with Open Boundaries
- Structure of the conservation laws in integrable spin chains with short range interactions
- Strong zero modes and eigenstate phase transitions in the XYZ/interacting Majorana chain
- Mapping out of equilibrium into equilibrium in one-dimensional transport models
- Long coherence times for edge spins
- Prethermal Strong Zero Modes and Topological Qubits
- Integrable approach to simple exclusion processes with boundaries. Review and progress
- Dynamics of almost strong edge modes in spin chains away from integrability
- Long-lived period-doubled edge modes of interacting and disorder-free Floquet spin chains
- Almost strong 0, π edge modes in clean, interacting 1D Floquet systems
- Derivation of a Matrix Product Representation for the Asymmetric Exclusion Process from Algebraic Bethe Ansatz
- Enhancing correlation times for edge spins through dissipation
- Strong zero modes in a class of generalised Ising spin ladders with plaquette interactions
- Dephasing enhanced strong Majorana zero modes in 2D and 3D higher-order topological superconductors
Cited by in corpus (6)
- Decay rates of almost strong modes in Floquet spin chains beyond Fermi's Golden Rule
- Slowly decaying zero mode in a weakly non-integrable boundary impurity model
- Subradiant edge states in an atom chain with waveguide-mediated hopping
- Non-Bloch dynamics and topology in a classical non-equilibrium process
- Floquet Product Mode
- Strong zero modes in integrable spin-S chains