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Entanglement temperature and entanglement entropy of excited states

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Abstract

We derive a general relation between the ground state entanglement Hamiltonian and the physical stress tensor within the path integral formalism. For spherical entangling surfaces in a CFT, we reproduce the local ground state entanglement Hamiltonian derived by Casini, Huerta and Myers. The resulting reduced density matrix can be characterized by a spatially varying “entanglement temperature”. Using the entanglement Hamiltonian, we calculate the first order change in the entanglement entropy due to changes in conserved charges of the ground state, and find a local first law-like relation for the entanglement entropy. Our approach provides a field theory derivation and generalization of recent results obtained by holographic techniques. However, we note a discrepancy between our field theoretically derived results for the entanglement entropy of excited states with a non-uniform energy density and current holographic results in the literature. Finally, we give a CFT derivation of a set of constraint equations obeyed by the entanglement entropy of excited states in any dimension. Previously, these equations were derived in the context of holography.

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Authors and Affiliations

  1. Department of Physics, University of Virginia, Box 400714, Charlottesville, Virginia, 22904, United States

    Gabriel Wong, Israel Klich & Diana Vaman

  2. Michigan Center for Theoretical Physics, University of Michigan, Ann Arbor, MI, 48109, United States

    Leopoldo A. Pando Zayas

Authors
  1. Gabriel Wong
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  2. Israel Klich
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  3. Leopoldo A. Pando Zayas
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  4. Diana Vaman
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Correspondence to Gabriel Wong.

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ArXiv ePrint: 1305.3291

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Wong, G., Klich, I., Zayas, L.A.P. et al. Entanglement temperature and entanglement entropy of excited states. J. High Energ. Phys. 2013, 20 (2013). https://doi.org/10.1007/JHEP12(2013)020

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  • DOI: https://doi.org/10.1007/JHEP12(2013)020

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