2013/05/31 by Gabriel Wong, Israel Klich, Leopoldo A. Pando Zayas +1 · 2 citations
Physics and Astronomy · #cond-mat.stat-mech #hep-th #quant-ph
paper · pdf · doi:10.1007/jhep12(2013)020
17 pages, 3 figures. Typo fixed in eq. (III.12) and constraint equation (VI.18) added generalizing previous result to higher dimensions.Some references added
arxiv created 2013/08/27 · arxiv updated 2014/05/05
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.