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 quasiperiodic o...

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Bibliographic Details
Published inProgress of theoretical and experimental physics Vol. 2024; no. 9
Main Authors Okunishi, Kouichi, Nishino, Tomotoshi
Format Journal Article
LanguageEnglish
Published Oxford University Press 18.09.2024
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Summary: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 quasiperiodic 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 a 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 short-distance behavior rapidly loses its accuracy.
ISSN:2050-3911
2050-3911
DOI:10.1093/ptep/ptae137