2016/08/31 by Ching Hua Lee, Dai Ozaki, Hiroaki Matsueda
Mathematics · Physics and Astronomy · #Ansatz #Black Holes and Theoretical Physics #Critical exponent #Critical phenomena #Critical point (mathematics) #Exponent #Fractal #Geometry #Mathematical analysis #Mathematical physics #Mathematics #Phase transition #Physics #Quantum #Quantum entanglement #Quantum many-body systems #Quantum mechanics #Renormalization #Renormalization group #Scale invariance #Scaling #Statistical physics #Theoretical and Computational Physics #Theoretical physics #cond-mat.stat-mech
paper · pdf · doi:10.1103/physreve.94.062144
published as Phys. Rev. E 94, 062144 (2016) · 13 pages, 8 figures
openalex created_date 2016/09/16 · arxiv created 2016/11/28 · openalex publication_date 2016/12/28 · arxiv updated 2017/01/04 · openalex updated_date 2026/08/05
Critical systems have always intrigued physicists and precipitated the development of new techniques. Recently, there has been renewed interest in the information contained in the configurations of classical critical systems, whose computation do not require full knowledge of the wave function. 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 Σ 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.