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Multipartitioning topological phases by vertex states and quantum entanglement

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arxiv 2110.11980 v1 pith:EYM5XTJY submitted 2021-10-22 cond-mat.str-el hep-thquant-ph

classification cond-mat.str-elhep-thquant-ph
keywords statestopologicaldensityentanglemententropymatrixmeasuresphases
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abstract

We discuss multipartitions of the gapped ground states of (2+1)-dimensional topological liquids into three (or more) spatial regions that are adjacent to each other and meet at points. By considering the reduced density matrix obtained by tracing over a subset of the regions, we compute various correlation measures, such as entanglement negativity, reflected entropy, and associated spectra. We utilize the bulk-boundary correspondence to show that such multipartitions can be achieved by using what we call vertex states in (1+1)-dimensional conformal field theory -- these are a type of state used to define an interaction vertex in string field theory and can be thought of as a proper generalization of conformal boundary states. This approach allows an explicit construction of the reduced density matrix near the entangling boundaries. We find the fingerprints of topological liquid in these quantities, such as (universal pieces in) the scaling of the entanglement negativity, and a non-trivial distribution of the spectrum of the partially transposed density matrix. For reflected entropy, we test the recent claim that states the difference between reflected entropy and mutual information is given, once short-range correlations are properly removed, by $(c/3)\ln 2$ where $c$ is the central charge of the topological liquid that measures ungappable edge degrees of freedom. As specific examples, we consider topological chiral $p$-wave superconductors and Chern insulators. We also study a specific lattice fermion model realizing Chern insulator phases and calculate the correlation measures numerically, both in its gapped phases and at critical points separating them.

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Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Entanglement in Presence of Topological Interfaces and Dualities

    hep-th 2026-07 conditional novelty 7.0 of 10

    Duality interfaces in 2d CFT project the vacuum entanglement spectrum onto a single symmetry sector, making the interface itself a physical symmetry-resolution filter.

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