Entanglement temperature and entanglement entropy of excited states

By Gabriel Wong, Israel Klich, L. A. Zayas, D. Vaman. 2013

229 citations recorded by the source corpus.

A bstractWe 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.

Subfields: Astronomy and Astrophysics, Atomic and Molecular Physics, and Optics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/49bcf6cfc8684c44508b47ad5ab6f392657d2683

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Citations in the corpus

Analyticity and the Unruh effect: a study of local modular flow (2024, unknown): “…theory (CFT) restricted to a ball in a conformally flat spacetime [10–12]; (ii) a global thermal state in two-dimensional CFT restricted to a Rindler wedge in Minkowski spacetime [13]; and (iii) a global thermal state in two-dimensional CFT restricted to an interval in Minkowski spacetime [14, 15].”
Entanglement of local operators in large-N conformal field theories (2014, unknown): “nt entropy which is peculiar to strongly coupled large NCFTs. To motivate our work further, note that a universal relation similar to the ﬁrst law of thermodynamics, called the ﬁrst law-like relation [11, 12, 13, 14], has been known for an 2 excited state produced by a small perturbation.2 However, ”
Modular Hamiltonians on the null plane and the Markov property of the vacuum state (2017, background): “This property has been the subject of much of the recent interest and applications of modular Hamiltonians; see for example [1, 2, 3, 4, 5, 6, 7, 8, 9].”
Entropy, extremality, euclidean variations, and the equations of motion (2017, methodology): “In order to derive the equations of motion from the first law of entanglement of [14, 15], one has to understand the modular Hamiltonian.”
Black hole chemistry: thermodynamics with Lambda (2016, background): “showing that entanglement entropy in CFTs satisfy a first law [240, 241].”
Universality of Gravity from Entanglement (2014, background): “[12] J.”