Holographic analysis of boundary correlation functions for the hyperbolic-lattice Ising model

Abstract

We analyze boundary spin correlation functions of the hyperbolic-lattice Ising model from the holographic point of view. Using the corner-transfer-matrix renormalization group (CTMRG) method, we demonstrate that the boundary correlation function exhibits power-law decay with quasi-periodic oscillation, while the bulk correlation function always decays exponentially. On the basis of the geometric relation between the bulk correlation path and distance along the outer edge boundary, we find that scaling dimensions for the boundary correlation function can be well explained by the combination of the bulk correlation length and background curvatures inherent to the hyperbolic lattice. We also investigate the cutoff effect of the bond dimension in CTMRG, revealing that the long-distance behavior of the boundary spin correlation is accurately described even with a small bond dimension. In contrast, the sort-distance behavior rapidly loses its accuracy.

19 pages, 9 figures

References in corpus (45)

• Gauge Theory Correlators from Non-Critical String Theory
• Large N Field Theories, String Theory and Gravity
• Holographic Derivation of Entanglement Entropy from AdS/CFT
• Area laws for the entanglement entropy - a review
• Aspects of Holographic Entanglement Entropy
• AdS/CFT Correspondence and Symmetry Breaking
• Entanglement renormalization
• Entanglement Renormalization and Holography
• Holographic quantum error-correcting codes: Toy models for the bulk/boundary correspondence
• Tensor networks for complex quantum systems
• Holographic duality from random tensor networks
• Corner Transfer Matrix Renormalization Group Method
• Tensor Network Renormalization
• Hyperbolic Lattices in Circuit Quantum Electrodynamics
• Anti-de Sitter Space from Optimization of Path Integrals in Conformal Field Theories
• Corner Transfer Matrix Algorithm for Classical Renormalization Group
• Loop optimization for tensor network renormalization
• Simulating hyperbolic space on a circuit board
• Tensor network renormalization yields the multi-scale entanglement renormalization ansatz
• Quantum Simulation of Hyperbolic Space with Circuit Quantum Electrodynamics: From Graphs to Geometry
• Real Space Renormalization in Statistical Mechanics
• Renormalization of tensor networks using graph independent local truncations
• Developments in the Tensor Network -- from Statistical Mechanics to Quantum Entanglement
• $p$-adic AdS/CFT
• Correlation amplitude for S=1/2 XXZ spin chain in the critical region
• Hyper-invariant tensor networks and holography
• Geometric effects on critical behaviours of the Ising model
• Holography on tessellations of hyperbolic space
• Lattice Setup for Quantum Field Theory in AdS${}_2$
• Tensor Network and Black Hole
• Tensor network and ($p$-adic) AdS/CFT
• Corner Transfer Matrix Renormalization Group Method Applied to the Ising Model on the Hyperbolic Plane
• Ising model on hyperbolic lattice studied by corner transfer matrix renormalization group method
• Towards Explicit Discrete Holography: Aperiodic Spin Chains from Hyperbolic Tilings
• Entanglement branching operator
• Breitenlohner-Freedman bound on hyperbolic tilings
• Weak correlation effects in the Ising model on triangular-tiled hyperbolic lattices
• Phase Transition of the Ising model on a Hyperbolic Lattice
• Emergent Einstein Equation in p-adic CFT Tensor Networks
• Aperiodic spin chains at the boundary of hyperbolic tilings
• Boundary theories of critical matchgate tensor networks
• Mean-field universality class induced by weak hyperbolic curvatures
• Free Energy Analysis of Spin Models on Hyperbolic Lattice Geometries
• Statistical Mechanics Approach to the Holographic Renormalization Group: Bethe Lattice Ising Model and p-adic AdS/CFT
• Boundary-field-driven control of discontinuous phase transitions on hyperbolic lattices

Cited by in corpus (6)

• Emergence of a Boundary-Sensitive Phase in Hyperbolic Ising Models
• Holographic Foliations: Self-Similar Quasicrystals from Hyperbolic Honeycombs
• Entanglement scaling behaviors of free fermions on hyperbolic lattices
• A glimpse into the Ultrametric spectrum
• Tensor-Network study of Ising model on infinite hyperbolic dodecahedral lattice
• Holographic Aspects of Dynamical Mean-Field Theory