2014/12/11 by Somdeb Chakraborty, Parijat Dey, Sourav Karar +1 · 1 citation
Physics and Astronomy · #Black Holes and Theoretical Physics #Entropy (arrow of time) #Excited state #Noncommutative and Quantum Gravity Theories #Perturbation theory (quantum mechanics) #Quantum #Quantum entanglement #Quantum field theory #Quantum gravity #Quantum many-body systems #Scaling #Scaling dimension #hep-th
paper · pdf · doi:10.1007/jhep04(2015)133
published as JHEP 1504 (2015) 133 · 12 pages, no figure; v2: some typos fixed, few references added
arxiv created 2014/12/11 · openalex publication_date 2015/04/01 · arxiv updated 2015/05/14 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
A class of (2+1)-dimensional quantum many body system characterized by an anisotropic scaling symmetry (Lifshitz symmetry) near their quantum critical point can be described by a (3+1)-dimensional dual gravity theory with negative cosmological constant along with a massive vector field, where the scaling symmetry is realized by the metric as an isometry. We calculate the entanglement entropy of an excited state of such a system holographically, i.e., from the asymptotic perturbation of the gravity dual using the prescription of Ryu and Takayanagi, when the subsystem is sufficiently small. With suitable identifications, we show that this entanglement entropy satisfies an energy conservation relation analogous to the first law of thermodynamics. The non-trivial massive vector field here plays a crucial role and contributes to an additional term in the energy relation.