Entanglement entropy on finitely ramified graphs
arXiv:1808.10391 · doi:10.1103/PhysRevD.98.106003
Abstract
We compute the entanglement entropy in a composite system separated by a finitely ramified boundary with the structure of a self-similar lattice graph. We derive the entropy as a function of the decimation factor which determines the spectral dimension, the latter being generically different from the topological dimension. For large decimations, the graph becomes increasingly dense, yielding a gain in the entanglement entropy which, in the asymptotically smooth limit, approaches a constant value. Conversely, a small decimation factor decreases the entanglement entropy due to a large number of spectral gaps which regulate the amount of information crossing the boundary. In line with earlier studies, we also comment on similarities with certain holographic formulations. Finally, we calculate the higher order corrections in the entanglement entropy which possess a log-periodic oscillatory behavior.
arXiv comment7 pages, 3 figures, references added, to be published in PRD
References in corpus (44)
- Holographic Derivation of Entanglement Entropy from AdS/CFT
- Area laws for the entanglement entropy - a review
- Aspects of Holographic Entanglement Entropy
- Entropy and Area
- A Covariant Holographic Entanglement Entropy Proposal
- Entanglement entropy and conformal field theory
- Entanglement in a simple quantum phase transition
- Building up spacetime with quantum entanglement
- Entanglement Renormalization and Holography
- Spectral Dimension of the Universe in Quantum Gravity at a Lifshitz Point
- Discrete scale invariance and complex dimensions
- Entanglement entropy of black holes
- Emergence of a 4D World from Causal Quantum Gravity
- Kirchhoff's Rule for Quantum Wires
- Quantum Noise as an Entanglement Meter
- Quantum Graphs: Applications to Quantum Chaos and Universal Spectral Statistics
- Holographic Entanglement Entropy
- Simulation of strongly correlated fermions in two spatial dimensions with fermionic Projected Entangled-Pair States
- Dynamically Triangulating Lorentzian Quantum Gravity
- Fractal universe and quantum gravity
- Bipartite Fluctuations as a Probe of Many-Body Entanglement
- Fractal Spacetime Structure in Asymptotically Safe Gravity
- Measuring entanglement entropy of a generic many-body system with a quantum switch
- Quantum Graphs II: Some spectral properties of quantum and combinatorial graphs
- Fermionic entanglement in itinerant systems
- Fractal space-times under the microscope: A Renormalization Group view on Monte Carlo data
- Log-periodic route to fractal functions
- Thermodynamics of photons on fractals
- Entanglement production in bosonic systems: Linear and logarithmic growth
- Functionals of the Brownian motion, localization and metric graphs
- Heat Kernels and Zeta Functions on Fractals
- Physical Consequences of Complex Dimensions of Fractals
- Localization in random fractal lattices
- Phase Transition of the Ising Model on Fractal Lattice
- The Renyi Entropy and the Multifractal Spectrum of Systems Near the Localization Transition
- Imprint of quantum gravity in the dimension and fabric of spacetime
- Finite Entanglement Entropy in Asymptotically Safe Quantum Gravity
- Zeta functions of quantum graphs
- Area law for random graph states
- Entangling Fractals
- Entropy of random entangling surfaces
- Mutual information and Bose-Einstein condensation
- Entanglement and area law with a fractal boundary in a topologically ordered phase
- Holography, Fractals and the Weyl Anomaly