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arXiv:2606.19437

Many-Body Protection of Topological Edge Memory in Strong Interacting Quenches

Yuxiao Hang, Stephan Haas, Rishabh Jha

cond-mat.str-elcond-mat.stat-mechquant-phSubmitted Jun 17, 2026• Announced Jun 19, 2026• 0 citations
v1 · Jun 17, 2026v2 · Jul 25, 2026
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Abstract

Quantum quenches drive edge states far from equilibrium, yet whether the memory of a topological initial state survives in a non-integrable, interacting system has remained largely unexplored. We study this question in the bond-alternating XXZ chain -- an interacting Su--Schrieffer--Heeger model hosting symmetry-protected topological edge modes with markedly enhanced boundary magnetization -- and analyze quenches across all combinations of single-particle and many-body initial and final Hamiltonians. The results organize by a single distinction as we rigorously establish in this work: whether the post-quench Hamiltonian is free or genuinely interacting. For a free post-quench Hamiltonian, the dynamics is solved exactly by a correlation-matrix approach; the boundary-mode return amplitude decays as $t^{-3/2}$, and initial interactions enter only through a dressed one-body density matrix. For a genuinely interacting post-quench Hamiltonian, finite-time stability bounds prove that away from local resonances the first-dimer magnetization remains stable on time windows growing as arbitrarily large powers of the inverse inter-dimer coupling. Matrix product state simulations across all four protocols show that interactions in the final Hamiltonian markedly extend finite-time boundary memory -- with local suppression near the isotropic $SU(2)$ point -- revealing a many-body protection mechanism in a non-integrable system where scrambling would otherwise wash out initial-state memory fast.

Comments
16+17 pages, 9+8 figures

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Almost strong edge-mode operators arising at the boundaries of certain interacting one-dimensional symmetry protected topological phases with Z_{2} symmetry have infinite temperature lifetimes that are nonperturbatively long in the integrability breaking terms, making them promising as bits for quantum information processing. We extract the lifetime of these edge-mode operators for small system sizes as well as in the thermodynamic limit. For the latter, a Lanczos scheme is employed to map the operator dynamics to a one-dimensional tight-binding model of a single particle in Krylov space. We find this model to be that of a spatially inhomogeneous Su-Schrieffer-Heeger model with a hopping amplitude that increases away from the boundary, and a dimerization that decreases away from the boundary. We associate this dimerized or staggered structure with the existence of the almost strong mode. Thus, the short time dynamics of the almost strong mode is that of the edge mode of the Su-Schrieffer-Heeger model, while the long time dynamics involves decay due to tunneling out of that mode, followed by chaotic operator spreading. We also show that competing scattering processes can lead to interference effects that can significantly enhance the lifetime.
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We investigate topological signatures in the short-time non-equilibrium dynamics of symmetry protected topological (SPT) systems starting from initial states which break the protecting symmetry. Naïvely, one might expect that topology loses meaning when a protecting symmetry is broken. Defying this intuition, we illustrate, in an interacting Su-Schrieffer-Heeger (SSH) model, how this combination of symmetry breaking and quench dynamics can give rise to both single-particle and many-body signatures of topology. From the dynamics of the symmetry broken state, we find that we are able to dynamically probe the equilibrium topological phase diagram of a symmetry respecting projection of the post-quench Hamiltonian. In the ensemble dynamics, we demonstrate how spontaneous symmetry breaking (SSB) of the protecting symmetry can result in a quantized many-body topological `invariant' which is not pinned under unitary time evolution. We dub this `dynamical many-body topology' (DMBT). We show numerically that both the pure state and ensemble signatures are remarkably robust, and argue that these non-equilibrium signatures should be quite generic in SPT systems, regardless of protecting symmetries or spatial dimension.
Long-lived π\piπ edge modes of interacting and disorder-free Floquet spin chains
Floquet spin chains have been a venue for understanding topological states of matter that are qualitatively different from their static counterparts by, for example, hosting π\piπ edge modes that show stable period-doubled dynamics. However the stability of these edge modes to interactions has traditionally required the system to be many-body localized in order to suppress heating. In contrast, here we show that even in the absence of disorder, and in the presence of bulk heating, π\piπ edge modes are long lived. Their lifetime is extracted from exact diagonalization and is found to be non-perturbative in the interaction strength. A tunneling estimate for the lifetime is obtained by mapping the stroboscopic time-evolution to dynamics of a single particle in Krylov subspace. In this subspace, the π\piπ edge mode manifests as the quasi-stable edge mode of an inhomogeneous Su-Schrieffer-Heeger model whose dimerization vanishes in the bulk of the Krylov chain.
The time evolution of topological systems is an active area of interest due to their expected applications in fault-tolerant quantum computing. Here, we analyze the dynamics of a noninteracting spinless fermion chain in its topological phase, quenched out of equilibrium by a Hamiltonian belonging to the same symmetry class. Due to particle-hole symmetry, the bulk properties of the system remain intact throughout its evolution. However, the boundary properties may be drastically altered, with the initially localized Majorana edge modes extending across the chain. Up to a timescale t∗{t}^{*}t∗, identified by area-law behavior of the entanglement entropy, these extended edge modes are an example of exotic effects in topological systems out of equilibrium. Further, while local disorder can be utilized to preserve localization and increase t∗{t}^{*}t∗, we still identify nontrivial dynamics in the Majorana polarization and Loschmidt echo.
Spin chains with symmetry-protected edge modes are promising candidates to realize intrinsically robust physical qubits that can be used for the storage and processing of quantum information. In any experimental realization of such physical systems, weak perturbations in the form of induced interactions and disorder are unavoidable and can be detrimental to the stored information. At the same time, the latter may in fact be beneficial; for instance, by deliberately inducing disorder which causes the system to localize. We explore the potential of using an XZX cluster Hamiltonian to encode quantum information into the local edge modes and comprehensively investigate the influence of both many-body interactions and disorder on their stability over time, adding substance to the narrative that many-body localization may stabilize quantum information. We recover the edge state at each time step, allowing us to reconstruct the quantum channel that captures the locally constrained out-of-equilibrium time evolution. With this representation in hand, we analyze how well classical and quantum information are preserved over time as a function of disorder and interactions. We find that the performance of the edge qubits varies dramatically between disorder realizations. Whereas some show a smooth decoherence over time, a sizable fraction is rapidly rendered unusable as memories. We also find that the stability of the classical information-a precursor for the usefulness of the chain as a quantum memory-depends strongly on the direction in which the bit is encoded. When employing the chain as a genuine quantum memory, encoded qubits are most faithfully recovered for low interaction and high disorder.