Random Fractal Ansatz for the configurations of Two-Dimensional Critical Systems

Abstract

Critical systems have always intrigued physicists and precipitated the development of new techniques. Recently, there has been renewed interest in the information contained in their classical configurations, whose computation do not require full knowledge of the wavefunction. Inspired by holographic duality, we investigated the entanglement properties of the classical configurations (snapshots) of the Potts model by introducing an ansatz ensemble of random fractal images. By virtue of the central limit theorem, our ansatz accurately reproduces the entanglement spectra of actual Potts snapshots without any fine-tuning of parameters or artificial restrictions on ensemble choice. It provides a microscopic interpretation of the results of previous studies, which established a relation between the scaling behavior of snapshot entropy and the critical exponent. More importantly, it elucidates the role of ensemble disorder in restoring conformal invariance, an aspect previously ignored. Away from criticality, the breakdown of scale invariance leads to a renormalization of the parameter $\Sigma$ in the random fractal ansatz, whose variation can be used as an alternative determination of the critical exponent. We conclude by providing a recipe for the explicit construction of fractal unit cells consistent with a given scaling exponent.

arXiv comment13 pages, 8 figures

References in corpus (28)

• Gauge Theory Correlators from Non-Critical String Theory
• Holographic Derivation of Entanglement Entropy from AdS/CFT
• Aspects of Holographic Entanglement Entropy
• Lectures on holographic methods for condensed matter physics
• Calculation of reduced density matrices from correlation functions
• Relativistic viscous hydrodynamics, conformal invariance, and holography
• Holographic duality with a view toward many-body physics
• Bekenstein-Hawking Entropy and Strange Metals
• Hidden Fermi surfaces in compressible states of gauge-gravity duality
• SLE for theoretical physicists
• What can gauge-gravity duality teach us about condensed matter physics?
• A Guide to Stochastic Loewner Evolution and its Applications
• Holographic Superfluids and the Dynamics of Symmetry Breaking
• Memory matrix theory of magnetotransport in strange metals
• Introduction to Holographic Superconductor Models
• The dynamics of quantum criticality via Quantum Monte Carlo and holography
• Scale-invariant hyperscaling-violating holographic theories and the resistivity of strange metals with random-field disorder
• Hydrodynamic transport in strongly coupled disordered quantum field theories
• Entanglement spectrum and Wannier center flow of the Hofstadter problem
• Holographic duality between $(2+1)$-d quantum anomalous Hall state and $(3+1)$-d topological insulators
• Exact holographic mapping in free fermion systems
• Position momentum Duality in the Entanglement Spectrum of Free Fermions
• Geometric Exponents, SLE and Logarithmic Minimal Models
• Exact Mapping from Singular Value Spectrum of Fractal Images to Entanglement Spectrum of One-Dimensional Quantum Systems
• Snapshot spectrum and critical phenomenon for two-dimensional classical spin systems
• Entanglement renormalization and integral geometry
• Entropy of Factorized Snapshot Data for Two-Dimensional Classical Spin Models
• Comment on "Snapshot spectrum and critical phenomenon for two-dimensional classical spin systems"

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