Anomalous Mixed-State Floquet Topology in One-Dimensional Open Quantum Systems

• URL: http://arxiv.org/abs/2604.25248v1
• Date: Tue, 28 Apr 2026 05:54:40 GMT
• Title: Anomalous Mixed-State Floquet Topology in One-Dimensional Open Quantum Systems
• Abstract summary: We investigate the non-equilibrium topology of a periodically driven, dissipative Su-Schrieffer-Heeger chain.<n>We show that the steady state can be characterised by a Hermitian purity spectrum.<n>We identify a pair of topological invariants $(0_mathrmEGP, _mathrmEGP)$, revealing a structure consistent with a $mathbbZtimesmathbbZ$ classification known from isolated Floquet SSH systems.
• Score: 41.99844472131922
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We investigate the non-equilibrium topology of a periodically driven, dissipative Su-Schrieffer-Heeger chain using the ensemble geometric phase (EGP) $φ_{\mathrm{EGP}}$-a generalisation of the Zak phase to open quantum systems. In contrast to earlier work, we use Floquet-Born-Markov theory to describe the coupling to thermal reservoirs microscopically. We show that the steady state can be characterised by a Hermitian purity spectrum, providing a direct analogue of band topology for mixed states. The periodic drive induces nontrivial winding and a quasienergy spectrum with distinct $0$ and $π$ band gaps, with protected edge modes in each gap. We identify a pair of topological invariants $(φ^{0}_{\mathrm{EGP}}, Δφ^π_{\mathrm{EGP}})$, revealing a structure consistent with a $\mathbb{Z}\times\mathbb{Z}$ classification known from isolated Floquet SSH systems, and show how it extends to a dissipative, finite-temperature setting in regimes where the steady-state structure remains well defined. Our results demonstrate when and how known Floquet topology survives in a driven-dissipative Gaussian steady state and establish Floquet topology as a robust concept beyond isolated zero-temperature systems. The underlying formalism provides a general framework for quadratic fermionic systems with linear bath couplings.

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