Entanglement Temperature and Entanglement Entropy of Excited States

Understand

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 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.