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Diagnosing 2D symmetry protected topological states via mixed state anomaly
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abstract
Symmetry-protected topological (SPT) phases are short-range entangled quantum states characterized by anomalous edge behavior, a manifestation of the bulk-boundary correspondence for topological phases. Moreover, the Li-Haldane conjecture posits that the entanglement spectrum exhibits the same anomaly as the physical edge spectrum, thereby serving as an entanglement-based fingerprint for identifying topological phases. In this work, we extend the entanglement-based diagnostic tools by demonstrating that the edge anomaly is manifested not only in the entanglement spectrum but also in the reduced density matrix itself, a phenomenon we refer to as the mixed state anomaly. Focusing on the two-dimensional $\mathbb{Z}_2$ SPT phase, we show that this anomaly is subtly encoded in symmetry-twisted mixed states, leading to a topological contribution to the disorder parameter beyond the area law, as well as a spontaneous-symmetry-breaking type long-range order when time reversal symmetry is present.
Forward citations
Cited by 5 Pith papers
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From Topological Order to Mixed-State Phases: A Ground-State Probe of Fractionalized Excitations
The RDM of 2D topological order at an entanglement cut realizes a 1D Z2 SW-SSB mixed-state phase whose correlations and disorder parameters encode anyon deconfinement and spinon fractionalization.
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Anomaly and symmetry-charge flow in mixed states
The chiral anomaly is extended to mixed states via symmetry-charge flow derived algebraically from symmetry and flux-insertion operators, restoring universality for Abelian symmetries in fermionic and bosonic systems.
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Anomaly and symmetry-charge flow in mixed states
Abelian mixed-state anomalies are fixed solely by an algebraic relation between a symmetry and its flux-insertion operator, producing universal symmetry-charge flow across charge sectors.
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From Topological Order to Mixed-State Phases: A Ground-State Probe of Fractionalized Excitations
Reduced density matrices of 2D topological orders at entanglement cuts realize 1D mixed-state phases whose properties detect fractionalized excitations such as anyons and spinons.
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