Hierarchy of mixed symmetry protected topological states in extended cluster states under subsystem decoherence

• URL: http://arxiv.org/abs/2606.22507v1
• Date: Sun, 21 Jun 2026 14:02:42 GMT
• Title: Hierarchy of mixed symmetry protected topological states in extended cluster states under subsystem decoherence
• Abstract summary: We study the effect of subsystem decoherence to an extended cluster state which is a symmetry protected topological (SPT) phase.<n>We show that decoherence is not merely a destructive process, but can induce and organize series of nontrivial mixed-states.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We study the effect of subsystem decoherence to an extended cluster state which is a symmetry protected topological (SPT) phase. The model includes many subsystem $Z_2$ symmetries. We report that subsystem decoherence induces local charge fluctuations, leading to a mixed SPT state in the unaffected subsystems. If we start from the extended cluster state, hierarchical mixed-state SPT phases emerge in response to step-by-step subsystem decoherences. These mixed-state SPT phases keep strong symmetries the symmetry of which is protecting symmetries for the initial cluster SPT. Moreover, these SPTs can be characterized by Rényi-2 string orders. Then, as the subsystems are progressively decohered, the hierarchy of mixed-state SPT phases terminates in a $Z_2$ strong-to-weak spontaneous symmetry breaking (SWSSB) state on the final remaining subsystem, where a long-range entangled state appears, namely a glassy Greenberger-Horne-Zeilinger (GHZ) state. Our work demonstrates that decoherence is not merely a destructive process, but can induce and organize series of nontrivial mixed-states. This reveals a systematic route from mixed-state SPT order to SWSSB with the glassy GHZ-type long-range entanglement.

Related papers

• Nonlocality-induced critical-length hierarchy from non-Hermitian competition [48.9823527611878]
  In short-range systems formed by two coupled chains, competition leads to the critical-length law $N_csimln D$.<n>Here we show that long-range hoppings fundamentally reorganizes this critical behavior, producing a hierarchy of distinct scaling laws.<n>Our results offer a platform-independent framework testable in programmable topoelectrical circuits, photonic lattices and digital quantum simulators.
  arXiv  Detail & Related papers  (2026-08-03T18:00:18Z)
• Anomalous Mixed-State Floquet Topology in One-Dimensional Open Quantum Systems [41.99844472131922]
  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.
  arXiv  Detail & Related papers  (2026-04-28T05:54:40Z)
• Mixed-state Phases from Higher-order SSPTs with Kramers-Wannier Symmetry [2.8192634711676128]
  We investigate the mixed-state phases obtained by tracing out the bulk degrees of freedom of higher-order subsystem SPT phases protected by non-invertible symmetries.<n>We find that the resulting mixed states exhibit the coexistence of the symmetry-protected topological order and SW SSB.<n>We also use the interface as a probe to characterize the mixed state phases, and specifically, when there is no local modification to preserve the symmetries across the interface, the two sides of the interface are in distinct phases.
  arXiv  Detail & Related papers  (2026-03-03T19:13:06Z)
• Strong-to-weak spontaneous symmetry breaking and average symmetry protected topological order in the doubled Hilbert space [0.0]
  This study is an extended version of the cluster model in one dimension with $Zotimes Z$ symmetry.<n>By using a scheme that we propose, a strong symmetry protected topological (SPT) mixed state and double average SPT (ASPT) state are constructed.<n>We numerically demonstrate the emergence of the two mixed SPT states and find that a transition occurs between them tuned by the strength of decoherence.
  arXiv  Detail & Related papers  (2025-03-13T12:44:24Z)
• Strong-to-weak symmetry breaking states in stochastic dephasing stabilizer circuits [0.0]
  Under symmetry-respective decoherence, spontaneous strong-to-weak symmetry breaking can occur. This work provides a scheme to describe S SSB and other decoherence phenomena in the mixed state by employing the stabilizer formalism and the efficient numerical algorithm of Clifford circuits.
  arXiv  Detail & Related papers  (2024-08-08T06:03:23Z)
• Hierarchy of emergent cluster states by measurement from symmetry-protected-topological states with large symmetry to subsystem cat state [0.0]
  We propose it measurement-producing hierarchy emerging among correlated states by sequential subsystem projective measurements. We also verify the symmetry-reduction hierarchy by sequential subsystem projective measurements applied to large systems and large symmetric cluster SPT states.
  arXiv  Detail & Related papers  (2024-05-04T07:17:53Z)
• Three perspectives on entropy dynamics in a non-Hermitian two-state system [41.94295877935867]
  entropy dynamics as an indicator of physical behavior in an open two-state system with balanced gain and loss is presented. We distinguish the perspective taken in utilizing the conventional framework of Hermitian-adjoint states from an approach that is based on biorthogonal-adjoint states and a third case based on an isospectral mapping.
  arXiv  Detail & Related papers  (2024-04-04T14:45:28Z)
• Symmetry Protected Topological Phases of Mixed States in the Doubled Space [0.0]
  We study the interplay of symmetry and topology in quantum many-body mixed states. In a phenomenon not seen in pure states, mixed states can exhibit average symmetries. We study the patterns of spontaneous symmetry breaking ( SSB) of mixed states.
  arXiv  Detail & Related papers  (2024-03-20T03:40:28Z)
• Higher-Order Cellular Automata Generated Symmetry-Protected Topological Phases and Detection Through Multi-Point Strange Correlators [21.052345471463802]
  We introduce HOCA to quantum many-body physics and construct a series of symmetry-protected topological (SPT) phases of matter. We show that HOCA can generate not only well-understood SPTs with symmetries supported on either regular (e.g., line-like subsystems in the 2D cluster model) or fractal subsystems, but also a large class of unexplored SPTs with symmetries supported on more choices of subsystems.
  arXiv  Detail & Related papers  (2023-12-31T13:56:20Z)
• Entanglement phase transition due to reciprocity breaking without measurement or post-selection [59.63862802533879]
  EPT occurs for a system undergoing purely unitary evolution. We analytically derive the entanglement entropy out of and at the critical point for the $l=1$ and $l/N ll 1$ case.
  arXiv  Detail & Related papers  (2023-08-28T14:28:59Z)
• Noise-resilient Edge Modes on a Chain of Superconducting Qubits [103.93329374521808]
  Inherent symmetry of a quantum system may protect its otherwise fragile states. We implement the one-dimensional kicked Ising model which exhibits non-local Majorana edge modes (MEMs) with $mathbbZ$ parity symmetry. MEMs are found to be resilient against certain symmetry-breaking noise owing to a prethermalization mechanism.
  arXiv  Detail & Related papers  (2022-04-24T22:34:15Z)
• Non-Hermitian $C_{NH} = 2$ Chern insulator protected by generalized rotational symmetry [85.36456486475119]
  A non-Hermitian system is protected by the generalized rotational symmetry $H+=UHU+$ of the system. Our finding paves the way towards novel non-Hermitian topological systems characterized by large values of topological invariants.
  arXiv  Detail & Related papers  (2021-11-24T15:50:22Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.