Gabriel Wong, Israel Klich, Leopoldo A. Pando Zayas, Diana Vaman
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 \emph{local} ground state entanglement Hamiltonian derived by Casini, Huerta and Myers. The resulting reduced density matrix can be interpreted as a state of local thermal equilibrium with 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 generalized, 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 dynamical equations obeyed by the entanglement entropy of excited states in $d=2$. Previously, these equations were derived in the context of holography.
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http://arxiv.org/abs/1305.3291
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