Entanglement Entropy of Annulus in Three Dimensions
arXiv:1501.01293 · doi:10.1007/JHEP04(2015)072
Abstract
The entanglement entropy of an annulus is examined in a three-dimensional system with or without a gap. For a free massive scalar field theory, we numerically calculate the mutual information across an annulus. We also study the holographic mutual information in the CGLP background describing a gapped field theory. We discover four types of solutions as the minimal surfaces for the annulus and classify the phase diagrams by varying the inner and outer radii. In both cases, we find the mutual information satisfies the monotonicity dictated by the unitarity and decays exponentially fast as the gap scale is increased. We speculate this is a universal behavior in any gapped system.
arXiv comment29 pages, 13 figures, v2: references added, minor changes
References in corpus (40)
- Holographic Derivation of Entanglement Entropy from AdS/CFT
- Entanglement in quantum critical phenomena
- Topological entanglement entropy
- Detecting topological order in a ground state wave function
- Aspects of Holographic Entanglement Entropy
- Entropy and Area
- Geometric and Renormalized Entropy in Conformal Field Theory
- Towards a derivation of holographic entanglement entropy
- Generalized gravitational entropy
- Quantum Extremal Surfaces: Holographic Entanglement Entropy beyond the Classical Regime
- Quantum corrections to holographic entanglement entropy
- Holographic c-theorems in arbitrary dimensions
- Novel Local CFT and Exact Results on Perturbations of N=4 Super Yang Mills from AdS Dynamics
- Entanglement as a Probe of Confinement
- A finite entanglement entropy and the c-theorem
- A refinement of entanglement entropy and the number of degrees of freedom
- F-Theorem without Supersymmetry
- Entanglement entropy in gauge theories and the holographic principle for electric strings
- AdS Bubbles, Entropy and Closed String Tachyons
- AdS/CFT and Strong Subadditivity of Entanglement Entropy
- Entanglement and alpha entropies for a massive scalar field in two dimensions
- Entanglement Entropy of Gapped Phases and Topological Order in Three dimensions
- Ricci-flat Metrics, Harmonic Forms and Brane Resolutions
- On the integrability of Wilson loops in AdS_5 x S^5: Some periodic ansatze
- Entanglement Entropy: A Perturbative Calculation
- On Shape Dependence and RG Flow of Entanglement Entropy
- Universality in the geometric dependence of Renyi entropy
- Universal Thermal Corrections to Single Interval Entanglement Entropy for Conformal Field Theories
- Entanglement Entropy of a Massive Fermion on a Torus
- Topological Entanglement Entropy and Holography
- Exact and Numerical Results on Entanglement Entropy in (5+1)-Dimensional CFT
- Numerical determination of the entanglement entropy for free fields in the cylinder
- On shape dependence of holographic mutual information in AdS4
- Holographic Entanglement Entropy of Multiple Strips
- Universal Thermal Corrections to Entanglement Entropy for Conformal Field Theories on Spheres
- M-Branes and Metastable States
- Entanglement entropy, planar surfaces, and spectral functions
- Entanglement Entropy of Two Spheres
- Correlation Function of Circular Wilson Loops at Strong Coupling
- Mutual information on the fuzzy sphere
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- Is entanglement a probe of confinement?
- Entanglement entropy from entanglement contour: higher dimensions
- Formulas for Partial Entanglement Entropy
- On shape dependence of holographic entanglement entropy in AdS4/CFT3
- Holographic Mutual Information for Singular Surfaces
- Entanglement Entropy and Mutual Information of Circular Entangling Surfaces in 2 + 1-dimensional Quantum Lifshitz Model
- Capacity of entanglement and distribution of density matrix eigenvalues in gapless systems
- On the Shape Dependence of Entanglement Entropy
- Double-Trace Deformations and Entanglement Entropy in AdS
- Aspects of N-partite information in conformal field theories
- Towards an Entanglement Measure for Mixed States in CFTs Based on Relative Entropy
- Entanglement Entropy of Annulus in Holographic Thermalization
- Renormalized Entanglement Entropy on Cylinder
- Mutual information from modular flow in CFTs
- Disks globally maximize the entanglement entropy in dimensions