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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
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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 5 Pith papers

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  1. On symmetry-resolved generalized entropies

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    A new framework computes generalized charged moments and symmetry-resolved Rényi entropies for arbitrary excited states of the free compact boson CFT, benchmarked against the XX chain.

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  3. Entanglement of Inhomogeneous Free Bosons and Orthogonal Polynomials

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  4. 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.

  5. R\'enyi Entanglement of Purification and Half R\'enyi Reflected Entropy in Free Scalar Theory

    hep-th 2025-01 conditional novelty 5.0 of 10

    In a free scalar lattice model, numerical calculations show Rényi entanglement of purification is at least half the Rényi reflected entropy for 0 < n < 2 in the small subsystems tested.

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