Simulating Holographic Conformal Field Theories on Hyperbolic Lattices

Abstract

We demonstrate how table-top settings combining hyperbolic lattices with nonlinear dynamics universally encode aspects of the bulk-boundary-correspondence between gravity in anti-de-Sitter (AdS) space and conformal field theory (CFT). Our concrete and broadly applicable holographic toy model simulates gravitational self-interactions in the bulk and features an emergent CFT with nontrivial correlations on the boundary. We measure the CFT data contained in the two- and three-point functions and clarify how a thermal CFT is simulated through an effective black hole geometry. As a concrete example, we propose and simulate an experimentally feasible protocol to measure the holographic CFT using electrical circuits.

5 pages, published version

References in corpus (48)

• Gauge Theory Correlators from Non-Critical String Theory
• The Large N Limit of Superconformal Field Theories and Supergravity
• The Black Hole in Three Dimensional Space Time
• Topological Photonics
• Cool horizons for entangled black holes
• Time Reversal Invariant Topologically Insulating Circuits
• Topological properties of linear circuit lattices
• Hyperbolic Lattices in Circuit Quantum Electrodynamics
• Aspects of Black Hole Quantum Mechanics and Thermodynamics in 2+1 Dimensions
• Bulk and Boundary Dynamics in BTZ Black Holes
• Simulating hyperbolic space on a circuit board
• Crystallography of Hyperbolic Lattices
• Observation of novel topological states in hyperbolic lattices
• Quantum Simulation of Hyperbolic Space with Circuit Quantum Electrodynamics: From Graphs to Geometry
• Hyperbolic band theory
• Topological hyperbolic lattices
• Active topolectrical circuits
• Line-Graph Lattices: Euclidean and Non-Euclidean Flat Bands, and Implementations in Circuit Quantum Electrodynamics
• Interacting Qubit-Photon Bound States with Superconducting Circuits
• Automorphic Bloch theorems for hyperbolic lattices
• Hyperbolic Matter in Electrical Circuits with Tunable Complex Phases
• Hyperbolic band topology with non-trivial second Chern numbers
• Exotic Multifractal Conductance Fluctuations in Graphene
• Circuit Quantum Electrodynamics in Hyperbolic Space: From Photon Bound States to Frustrated Spin Models
• Hyperbolic Topological Band Insulators
• Universality of Hofstadter butterflies on hyperbolic lattices
• Chern insulator in a hyperbolic lattice
• Band theory and boundary modes of high-dimensional representations of infinite hyperbolic lattices
• Topological photonics: fundamental concepts, recent developments, and future directions
• Higher-order topological insulators in hyperbolic lattices
• Holography on tessellations of hyperbolic space
• Lattice Setup for Quantum Field Theory in AdS${}_2$
• Observation of cnoidal wave localization in non-linear topolectric circuits
• Higher-order Topological Hyperbolic Lattices
• Conformal Quasicrystals and Holography
• Non-Abelian hyperbolic band theory from supercells
• Quantum phase transitions of interacting bosons on hyperbolic lattices
• Selberg trace formula in hyperbolic band theory
• Density of states of tight-binding models in the hyperbolic plane
• Symmetry and topology of hyperbolic Haldane models
• Anderson localization transition in disordered hyperbolic lattices
• Towards Explicit Discrete Holography: Aperiodic Spin Chains from Hyperbolic Tilings
• Hyperbolic non-Abelian semimetal
• Central charges of aperiodic holographic tensor network models
• Breitenlohner-Freedman bound on hyperbolic tilings
• Aperiodic spin chains at the boundary of hyperbolic tilings
• Hyperbolic Lattice for Scalar Field Theory in AdS${}_3$
• Eigenmodes of the Laplacian on Hyperbolic Lattices

Cited by in corpus (19)

• Topological linear response of hyperbolic Chern insulators
• Hyperbolic lattices and two-dimensional Yang-Mills theory
• Kitaev model on Hurwitz hyperbolic tilings: A non-Abelian gapped chiral spin liquid
• Hyperbolic Spin Liquids
• Chiral Gapless Spin Liquid in Hyperbolic Space
• Deriving the non-perturbative gravitational dual of quantum Liouville theory from BCFT operator algebra
• Holographic Foliations: Self-Similar Quasicrystals from Hyperbolic Honeycombs
• Wormhole-induced effective coupling in SYK chains
• Non-Hermitian catalysis of spontaneous symmetry breaking on Euclidean and hyperbolic lattices
• Quantum geometric tensors from sub-bundle geometry
• Discrete JT gravity as an Ising model
• Walking on Archimedean Lattices: Insights from Bloch Band Theory
• Entanglement scaling behaviors of free fermions on hyperbolic lattices
• Clustering-induced localization of quantum walks on networks
• Tunable cornerlike states in topological type-II hyperbolic lattices
• Hofstadter's Butterfly in AdS${}_3$ Black Holes
• Topological states and flat bands in exactly solvable decorated Cayley trees
• Classical spin liquids from frustrated Ising models in hyperbolic space
• Discrete holography and density of states in the crossover from hyperbolic to Euclidean lattices