Holographic entanglement density for spontaneous symmetry breaking

Abstract

We investigate the properties of the holographic entanglement entropy of the systems in which the $U(1)$ or the translational symmetry is broken \textit{spontaneously}. For this purpose, we define the entanglement density of the strip-subsystems and examine both the first law of entanglement entropy (FLEE) and the area theorem. We classify the conditions that FLEE and/or the area theorem obey and show that such a classification may be useful for characterizing the systems. We also find universalities from both FLEE and the area theorem. In the spontaneous symmetry breaking case, FLEE is always obeyed regardless of the type of symmetry: $U(1)$ or translation. For the translational symmetry, the area theorem is always violated when the symmetry is weakly broken, independent of the symmetry breaking patterns (explicit or spontaneous). We also argue that the $\log$ contribution of the entanglement entropy from the Goldstone mode may not appear in the strongly coupled systems.

29 pages, 7 figures

References in corpus (28)

• Building an AdS/CFT superconductor
• Holographic c-theorems in arbitrary dimensions
• Entanglement entropy of fermions in any dimension and the Widom conjecture
• Seeing a c-theorem with holography
• A holographic proof of the strong subadditivity of entanglement entropy
• Topological order in a 3D toric code at finite temperature
• Holographic Entanglement Entropy in Insulator/Superconductor Transition
• Quantum Information in Holographic Duality
• Holographic Axion Model: a simple gravitational tool for quantum matter
• Holographic Entanglement Entropy in P-wave Superconductor Phase Transition
• Entanglement Entropy and Wilson Loop in Stückelberg Holographic Insulator/Superconductor Model
• Entanglement Entropy and Complexity for One-Dimensional Holographic Superconductors
• Bound of diffusion constants from pole-skipping points: spontaneous symmetry breaking and magnetic field
• Holographic entanglement entropy in general holographic superconductor models
• Pseudo-spontaneous $U(1)$ Symmetry Breaking in Hydrodynamics and Holography
• A Holographic Superfluid Symphony
• The breakdown of magneto-hydrodynamics near AdS${}_2$ fixed point and energy diffusion bound
• Homes' law in holographic superconductor with linear-$T$ resistivity
• Dissipation in Holographic Superfluids
• Entanglement Wedge Minimum Cross-section in Holographic Massive Gravity Theory
• Risking your NEC
• On Holographic Entanglement Density
• Holographic entanglement entropy in two-order insulator/superconductor transitions
• Holographic Observables at Large $d$
• Low temperature properties of holographic condensates
• Entanglement entropy and the first law at third order for boosted black branes
• Topological invariants of the Ryu-Takayanagi ($RT$) surface used to observe holographic superconductor phase transition
• Inverted c-functions in thermal states

Cited by in corpus (7)

• Quasi-normal modes of dyonic black holes and magneto-hydrodynamics
• Holographic study of $T\bar{T}$ like deformed HV QFTs: holographic entanglement entropy
• Thermal fluctuations of black holes with non-linear electrodynamics and charged Renyi entropy
• Bounding entanglement wedge cross sections
• Charge transport properties in a novel holographic quantum phase transition model
• Encoded information of mixed correlations: the views from one dimension higher
• Holographic entanglement entropy probe on spontaneous symmetry breaking with vector order