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 quasi-periodic 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 the 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 sort-distance behavior rapidly loses its accuracy.

19 pages, 9 figures

References in corpus (5)

• Holography on tessellations of hyperbolic space
• Ising model on hyperbolic lattice studied by corner transfer matrix renormalization group method
• Entanglement branching operator
• Weak correlation effects in the Ising model on triangular-tiled hyperbolic lattices
• Mean-field universality class induced by weak hyperbolic curvatures

Cited by in corpus (6)

• Emergence of a Boundary-Sensitive Phase in Hyperbolic Ising Models
• Holographic Foliations: Self-Similar Quasicrystals from Hyperbolic Honeycombs
• Entanglement scaling behaviors of free fermions on hyperbolic lattices
• A glimpse into the Ultrametric spectrum
• Tensor-Network study of Ising model on infinite hyperbolic dodecahedral lattice
• Holographic Aspects of Dynamical Mean-Field Theory