Tensor Network and Black Hole

Abstract

A tensor network formalism of thermofield dynamics is introduced. The formalism relates the original Hilbert space with its tilde space by a product of two copies of a tensor network. Then, their interface becomes an event horizon, and the logarithm of the tensor rank corresponds to the black hole entropy. Eventually, multiscale entanglement renormalization anzats (MERA) reproduces an AdS black hole at finite temperature. Our finding shows rich functionalities of MERA as efficient graphical representation of AdS/CFT correspondence.

6 pages, 4 figures

References in corpus (46)

• Holographic Derivation of Entanglement Entropy from AdS/CFT
• Entanglement in quantum critical phenomena
• Entropy and Area
• Matrix Product States, Projected Entangled Pair States, and variational renormalization group methods for quantum spin systems
• Geometric and Renormalized Entropy in Conformal Field Theory
• Entanglement entropy and conformal field theory
• Eternal Black Holes in AdS
• Entanglement renormalization
• Building up spacetime with quantum entanglement
• Thermodynamic limit of the density matrix renormalization for the spin-1 Heisenberg chain
• Classical simulation of infinite-size quantum lattice systems in one spatial dimension
• A class of quantum many-body states that can be efficiently simulated
• Entanglement Renormalization and Holography
• Black Hole Entropy in Canonical Quantum Gravity and Superstring Theory
• DMRG and periodic boundary conditions: a quantum information perspective
• Entanglement entropy of black holes
• Entanglement entropy of fermions in any dimension and the Widom conjecture
• Non-Fermi liquids from holography
• Violation of the entropic area law for Fermions
• The Gravity Dual of a Density Matrix
• A class of ansatz wave functions for 1D spin systems and their relation to DMRG
• Hidden Fermi surfaces in compressible states of gauge-gravity duality
• Entropy, entanglement, and area: analytical results for harmonic lattice systems
• Theory of finite-entanglement scaling at one-dimensional quantum critical points
• Algorithms for entanglement renormalization
• Finite Temperature Density Matrix Renormalization using an enlarged Hilbert space
• Scaling of entanglement support for Matrix Product States
• Tensor network states and geometry
• Black hole thermodynamics and information loss in two dimensions
• Holographic Fermi Surfaces and Entanglement Entropy
• DeSitter entropy, quantum entanglement and ADS/CFT
• Entanglement scaling in critical two-dimensional fermionic and bosonic systems
• Near Extremal Black Hole Entropy as Entanglement Entropy via AdS2/CFT1
• Entanglement renormalization, scale invariance, and quantum criticality
• Black hole entropy as entanglement entropy: a holographic derivation
• Scaling Behavior of Entanglement in Two- and Three-Dimensional Free Fermions
• Rindler Quantum Gravity
• Holographic Entanglement Entropy and Fermi Surfaces
• Universal crossovers between entanglement entropy and thermal entropy
• Entanglement entropy of black holes and AdS/CFT correspondence
• Area law and vacuum reordering in harmonic networks
• Bethe Ansatz for the Temperley-Lieb loop model with open boundaries
• The Bethe ansatz as a matrix product ansatz
• Holographic View on Quantum Correlations and Mutual Information between Disjoint Blocks of a Quantum Critical System
• Generalization of the matrix product ansatz for integrable chains
• Quantum states of the spacetime, and formation of black holes in AdS

Cited by in corpus (38)

• Tensor Network Renormalization
• Holographic Local Quenches and Entanglement Density
• Surface/State Correspondence as a Generalized Holography
• Lecture Notes of Tensor Network Contractions
• Simulating hyperbolic space on a circuit board
• Tensor network renormalization yields the multi-scale entanglement renormalization ansatz
• Deep Learning and AdS/CFT
• Developments in the Tensor Network -- from Statistical Mechanics to Quantum Entanglement
• Entanglement between Two Interacting CFTs and Generalized Holographic Entanglement Entropy
• Entanglement renormalization and wavelets
• AdS/CFT as a deep Boltzmann machine
• Spacetime symmetries and conformal data in the continuous multi-scale entanglement renormalization ansatz
• Global symmetries in tensor network states: symmetric tensors versus minimal bond dimension
• Symmetry protected entanglement renormalization
• Linear growth of entanglement entropy in holographic thermalization captured by horizon interiors and mutual information
• Information Geometry of Entanglement Renormalization for free Quantum Fields
• A theory of minimal updates in holography
• CFT sewing as the dual of AdS cut-and-paste
• Entanglement, Tensor Networks and Black Hole Horizons
• Holographic spin networks from tensor network states
• Generalized Exact Holographic Mapping with Wavelets
• Tensor network state correspondence and holography
• Duality and free energy analyticity bounds for few-body Ising models with extensive homology rank
• Thermal geometry from CFT at finite temperature
• Correspondence between Entanglement Growth and Probability Distribution of Quasi-Particles
• MERA as a holographic strange correlator
• Holographic analysis of boundary correlation functions for the hyperbolic-lattice Ising model
• Geometry and Dynamics of Emergent Spacetime from Entanglement Spectrum
• Holographic Interpretation of Shannon Entropy of Coherence of Quantum Pure States
• Banados-Teitelboim-Zanelli Black Hole in the Information Geometry
• Emergent geometry, thermal CFT and surface/state correspondence
• A new perspective to formulate a dissipative thermo field dynamics
• Strictly local tensor networks for short-range topological insulators
• Entanglement Renormalization of the class of Continuous Matrix Product States
• Correspondence between causality in flat Minkowski spacetime and entanglement in thermofield-double state: Hessian-geometrical study
• Entanglement renormalization for quantum fields with boundaries and defects
• Exact Mappings in Condensed Matter Physics
• The weak equivalence principle and the Dirac constant: A result from the holographic principle