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Renyi relative entropies and renormalization group flows

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arxiv 1807.03305 v2 pith:PQVTDMGR submitted 2018-07-09 hep-th cond-mat.stat-mechquant-ph

Horacio Casini , Raimel Medina , Ignacio Salazar , Gonzalo Torroba This is my paper · ORCID
classification hep-thcond-mat.stat-mechquant-ph
keywords grouprelativerenormalizationentropiesfieldflowsrenyitheory
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Quantum Renyi relative entropies provide a one-parameter family of distances between density matrices, which generalizes the relative entropy and the fidelity. We study these measures for renormalization group flows in quantum field theory. We derive explicit expressions in free field theory based on the real time approach. Using monotonicity properties, we obtain new inequalities that need to be satisfied by consistent renormalization group trajectories in field theory. These inequalities play the role of a second law of thermodynamics, in the context of renormalization group flows. Finally, we apply these results to a tractable Kondo model, where we evaluate the Renyi relative entropies explicitly. An outcome of this is that Anderson's orthogonality catastrophe can be avoided by working on a Cauchy surface that approaches the light-cone.

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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. Petz-R\'enyi relative entropy in QFT from modular theory

    math-ph 2024-11 conditional novelty 7.0 of 10

    Petz-Renyi relative entropy for coherent excitations of free quantum fields is computed from modular theory and shown to involve the symmetric part of the two-point function, unlike relative entropy.

  2. Renormalized AdS gravity and holographic entanglement entropy of even-dimensional CFTs

    hep-th 2019-08 conditional novelty 6.0 of 10

    Kounterterm renormalization is extended to even-dimensional holographic CFTs, yielding a universal entanglement entropy formula whose logarithmic coefficient reproduces the type A central charge.

  3. Quantum Renyi relative entropies on a spin chain with interface defects

    cond-mat.stat-mech 2019-08 conditional novelty 6.0 of 10

    For a free-fermion chain with a hopping defect, the quantum Renyi relative entropies are expressed as a fitted formula that depends on the effective central charge and subsystem size.

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