Entanglement temperature and entanglement entropy of excited states

被引:0
作者
Gabriel Wong
Israel Klich
Leopoldo A. Pando Zayas
Diana Vaman
机构
[1] University of Virginia,Department of Physics
[2] University of Michigan,Michigan Center for Theoretical Physics
来源
Journal of High Energy Physics | / 2013卷
关键词
Field Theories in Lower Dimensions; AdS-CFT Correspondence; Conformal and W Symmetry; Field Theories in Higher Dimensions;
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摘要
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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