Stochastic strong zero modes and their dynamical manifestations

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.

5+8 pages, 4 figures; v2 published version

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Cited by in corpus (6)

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• 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