Conformal Quasicrystals and Holography

Abstract

Recent studies of holographic tensor network models defined on regular tessellations of hyperbolic space have not yet addressed the underlying discrete geometry of the boundary. We show that the boundary degrees of freedom naturally live on a novel structure, a conformal quasicrystal, that provides a discrete model of conformal geometry. We introduce and construct a class of one-dimensional conformal quasicrystals, and discuss a higher-dimensional example (related to the Penrose tiling). Our construction permits discretizations of conformal field theories that preserve an infinite discrete subgroup of the global conformal group at the cost of lattice periodicity.

v1: 8 pages, 4 figures; v2: 9 pages, 4 figures, expanded Introduction and Discussion, added references, matches version to be published in PRX

References in corpus (5)

• A class of quantum many-body states that can be efficiently simulated
• Entanglement renormalization, scale invariance, and quantum criticality
• Advances on Tensor Network Theory: Symmetries, Fermions, Entanglement, and Holography
• Loop Quantum Gravity, Exact Holographic Mapping, and Holographic Entanglement Entropy
• De Sitter Space as a Tensor Network: Cosmic No-Hair, Complementarity, and Complexity

Cited by in corpus (37)

• 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
• Holographic tensor network models and quantum error correction: A topical review
• Automorphic Bloch theorems for hyperbolic lattices
• Circuit Quantum Electrodynamics in Hyperbolic Space: From Photon Bound States to Frustrated Spin Models
• Universality of Hofstadter butterflies on hyperbolic lattices
• Lattice Setup for Quantum Field Theory in AdS${}_2$
• Effective Field Theory for Quasicrystals and Phasons Dynamics
• Symmetry and topology of hyperbolic Haldane models
• Selberg trace formula in hyperbolic band theory
• Towards Explicit Discrete Holography: Aperiodic Spin Chains from Hyperbolic Tilings
• Anderson localization transition in disordered hyperbolic lattices
• Simulating Holographic Conformal Field Theories on Hyperbolic Lattices
• Central charges of aperiodic holographic tensor network models
• Homogeneous Holographic Viscoelastic Models & Quasicrystals
• Tensor network models of AdS/qCFT
• Aperiodic spin chains at the boundary of hyperbolic tilings
• Topological linear response of hyperbolic Chern insulators
• Black Rubber and the Non-linear Elastic Response of Scale Invariant Solids
• Boundary theories of critical matchgate tensor networks
• Fault-tolerant logical gates in holographic stabilizer codes are severely restricted
• Holographic tensor networks from hyperbolic buildings
• Hyperbolic lattices and two-dimensional Yang-Mills theory
• Eigenmodes of the Laplacian on Hyperbolic Lattices
• Self-dual quasiperiodic percolation
• Wormhole-induced effective coupling in SYK chains
• Holographic Foliations: Self-Similar Quasicrystals from Hyperbolic Honeycombs
• Far from Perfect: Quantum Error Correction with (Hyperinvariant) Evenbly Codes
• Walking on Archimedean Lattices: Insights from Bloch Band Theory
• Entanglement scaling behaviors of free fermions on hyperbolic lattices
• Tessellation codes: encoded quantum gates by geometric rotation
• Discrete holography and density of states in the crossover from hyperbolic to Euclidean lattices
• Classical spin liquids from frustrated Ising models in hyperbolic space
• Biased-Noise Thresholds of Zero-Rate Holographic Codes with Tensor-Network Decoding
• Topological states and flat bands in exactly solvable decorated Cayley trees
• Critical spin models from holographic disorder