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Reflected entropy and computable cross-norm negativity: Free theories and symmetry resolution

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arxiv 2307.11009 v2 pith:KG6Q44EH submitted 2023-07-20 hep-th cond-mat.stat-mechcond-mat.str-elquant-ph

Clément Berthiere , Gilles Parez This is my paper · ORCID
classification hep-thcond-mat.stat-mechcond-mat.str-elquant-ph
keywords ccnrreflectedentropynegativitycomputablecross-normfreesymmetry
verification ladder T0 review T1 audit T2 compute T3 formal
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abstract

We investigate a separability criterion based on the computable cross-norm (CCNR), and a related quantity called the CCNR negativity. We introduce a reflected version of the CCNR negativity, and discuss its connection with other well-established entanglement-related quantities, namely the reflected entropy and the operator entanglement entropy. For free fermionic and bosonic theories, we derive exact formulas in terms of two-point correlation functions, which allow for systematic numerical investigations and, in principle, analytical treatments. For systems with a global $U(1)$ symmetry, we study the symmetry-resolved reflected entropy and CCNR negativity. We provide conformal field theory (CFT) results for the charged moments in the case of adjacent intervals, finding perfect agreement with the numerics. We observe an equipartition of reflected entropies and CCNR negativities, both for free-fermions and free-boson models. The first charge-dependent corrections are conjectured for fermions, and worked out from the CFT calculations for bosons.

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Cited by 3 Pith papers

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

  1. Surviving correlations across a horizon: reflected entropy for bosonic fields in non-inertial frames and black hole spacetimes

    hep-th 2026-08 conditional novelty 6.0 of 10

    Bosonic Alice-Bob reflected entropy saturates at nonzero floors (1.757 bits for Bell, 0.315 for GHZ) at infinite acceleration, while the inter-wedge reflected entropy diverges linearly in the squeezing parameter.

  2. Entanglement of Inhomogeneous Free Bosons and Orthogonal Polynomials

    cond-mat.stat-mech 2025-05 conditional novelty 6.0 of 10

    For inhomogeneous free-boson chains, the leading entanglement entropy is (a*/6) log N, where a* is the scaling exponent of the region where the local potential vanishes.

  3. Genuine multi-entropy and holography

    hep-th 2025-02 conditional novelty 6.0 of 10

    A new 'genuine multi-entropy' separates true q-party entanglement from lower-party pieces, and holographic systems are shown to carry O(1/G_N) genuine multipartite entanglement for connected regions.

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