Spurious Strange Correlators in Symmetry-Protected Topological Phases

• URL: http://arxiv.org/abs/2512.06691v1
• Date: Sun, 07 Dec 2025 06:54:45 GMT
• Title: Spurious Strange Correlators in Symmetry-Protected Topological Phases
• Authors: Wei-Liang Gao, Jie-Yu Zhang, Zheng-Xin Liu, Peng Ye,
• Abstract summary: Strange correlator is a powerful tool widely used in detecting symmetry-protected topological phases.<n>In this work, we report that an ill-chosen reference state can induce spurious long-range strange correlators in trivial SPT phases.
• Score: 14.135307469810144
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Strange correlator is a powerful tool widely used in detecting symmetry-protected topological (SPT) phases. However, the result of strange correlator crucially relies on the adoption of the reference state. In this work, we report that an ill-chosen reference state can induce spurious long-range strange correlators in trivial SPT phases, leading to false positives in SPT diagnosis. Using matrix product state (MPS) representation, we trace the origin of these spurious signals in trivial SPT phases to the magnitude-degeneracy of the transfer matrix. We systematically classify three distinct mechanisms responsible for such degeneracy, each substantiated by concrete examples: (1) the presence of high-dimensional irreducible representations in the entanglement space; (2) a phase mismatch in symmetry representations between the target and reference states; and (3) long-range order arising from symmetry breaking. Our findings clarify the importance of the choice of proper reference states, providing a guideline to avoid pitfalls and correctly identify SPT order using strange correlators.

Related papers

• Memorization, Emergence, and Explaining Reversal Failures: A Controlled Study of Relational Semantics in LLMs [43.414287127130684]
  We propose a synthetic framework that generates text from symmetric/inverse triples, trains GPT-style autoregressive models from scratch, and evaluate memorization, logical inference, and in-context generalization.<n>We find that relational semantics emerge with sufficient logic-bearing supervision, even in shallow (2-3 layer) models, and that successful generalization aligns with stable intermediate-layer signals.
  arXiv  Detail & Related papers  (2026-01-06T11:20:38Z)
• Identification of Causal Direction under an Arbitrary Number of Latent Confounders [54.76982125821112]
  In real-world scenarios, observed variables may be affected by multiple latent variables simultaneously.<n>We make use of the joint higher-order cumulant matrix of the observed variables constructed in a specific way.<n>We show that, surprisingly, causal asymmetry between two observed variables can be directly seen from the rank deficiency properties of such higher-order cumulant matrices.
  arXiv  Detail & Related papers  (2025-10-26T15:10:00Z)
• Symmetric entanglers for non-invertible SPT phases [0.0]
  We argue that a symmetric entangler should exist for $1+1$d systems whenever the non-invertible symmetry has SPT phases connected by fixed-charge dualities (FCD)<n>We construct an explicit example of a symmetric entangler for the two SPT phases with $mathrmRep(A_4)$-symmetry, as a matrix product unitary (MPU)
  arXiv  Detail & Related papers  (2025-09-04T18:03:57Z)
• Topological Phase Transitions and Mixed State Order in a Hubbard Quantum Simulator [36.556659404501914]
  Topological phase transitions challenge conventional paradigms in many-body physics.<n>We observe such a transition between one-dimensional crystalline symmetry-protected topological phases.<n>Our results demonstrate how topology and information influence quantum phase transitions.
  arXiv  Detail & Related papers  (2025-05-22T17:58:35Z)
• Strange correlator and string order parameter for non-invertible symmetry protected topological phases in 1+1d [0.0]
  We construct strange correlators and string order parameters for non-invertible symmetry protected topological phases.<n>We show that strange charged operators inserted into the strange correlator are linked to the interface algebra.<n>We show that the entanglement spectrum degeneracy is determined by the irreducible representations of the interface algebra.
  arXiv  Detail & Related papers  (2025-05-01T17:26:43Z)
• Higher-Form Anomalies Imply Intrinsic Long-Range Entanglement [0.0]
  We show that generic gapped quantum many-body states which respect an anomalous finite higher-form symmetry have an exponentially small overlap with any short-range entangled (SRE) state.<n>We also identify a new (3+1)D intrinsic mixed-state topological order that does not obey remote-detectability by local decoherence of the (3+1)D Toric Code with fermionic loop excitations.
  arXiv  Detail & Related papers  (2025-04-14T18:00:00Z)
• Predicting symmetries of quantum dynamics with optimal samples [41.42817348756889]
  Identifying symmetries in quantum dynamics is a crucial challenge with profound implications for quantum technologies.<n>We introduce a unified framework combining group representation theory and subgroup hypothesis testing to predict these symmetries with optimal efficiency.<n>We prove that parallel strategies achieve the same performance as adaptive or indefinite-causal-order protocols.
  arXiv  Detail & Related papers  (2025-02-03T15:57:50Z)
• Topological nature of edge states for one-dimensional systems without symmetry protection [46.87902365052209]
  We numerically verify and analytically prove a winding number invariant that correctly predicts the number of edge states in one-dimensional, nearest-neighbor (between unit cells)<n>Our winding number is invariant under unitary or similarity transforms.
  arXiv  Detail & Related papers  (2024-12-13T19:44:54Z)
• 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)
• Emergence of non-Abelian SU(2) invariance in Abelian frustrated fermionic ladders [37.69303106863453]
  We consider a system of interacting spinless fermions on a two-leg triangular ladder with $pi/2$ magnetic flux per triangular plaquette. Microscopically, the system exhibits a U(1) symmetry corresponding to the conservation of total fermionic charge, and a discrete $mathbbZ$ symmetry. At the intersection of the three phases, the system features a critical point with an emergent SU(2) symmetry.
  arXiv  Detail & Related papers  (2023-05-11T15:57:27Z)
• Symmetry protected topological phases under decoherence [0.0]
  In particular, we study a class of symmetry protected topological (SPT) phases under various types of decoherence.<n>We demonstrate that the system can still retain the nontrivial topological information from the SPT ground state even under decoherence.
  arXiv  Detail & Related papers  (2022-10-28T18:00:00Z)
• Bulk-boundary correspondence for intrinsically-gapless SPTs from group cohomology [3.299672391663527]
  Intrinsically gapless symmetry protected topological phases (igSPT) are gapless systems with SPT edge states. An anomaly in the low-energy (IR) symmetry group emerges from an extended anomaly-free microscopic (UV) symmetry. In two- and three-dimensional systems, an additional possibility is that the emergent anomaly can be satisfied by an anomalous symmetry-enriched topological order.
  arXiv  Detail & Related papers  (2022-08-18T18:00:04Z)
• Boundary theories of critical matchgate tensor networks [59.433172590351234]
  Key aspects of the AdS/CFT correspondence can be captured in terms of tensor network models on hyperbolic lattices. For tensors fulfilling the matchgate constraint, these have previously been shown to produce disordered boundary states. We show that these Hamiltonians exhibit multi-scale quasiperiodic symmetries captured by an analytical toy model.
  arXiv  Detail & Related papers  (2021-10-06T18:00:03Z)

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.