SciPost Physics

SciPost Phys. 15, 218 (2023) · published 30 November 2023

• doi: 10.21468/SciPostPhys.15.5.218
• pdf
• BiBTeX
• RIS
• Submissions/Reports
• 

Abstract

In view of making progress towards establishing a holographic duality for theories defined on a discrete tiling of the hyperbolic plane, we consider a recently proposed boundary spin chain Hamiltonian with aperiodic couplings that are chosen such as to reflect the inflation rule, i.e. the construction principle, of the bulk tiling. As a remnant of conformal symmetry, the spin degrees of freedom are arranged in multiplets of the dihedral group under which the bulk lattice is invariant. For the boundary Hamiltonian, we use strong-disorder RG techniques and evaluate correlation functions, the entanglement entropy and mutual information for the case that the ground state is in an aperiodic singlet phase. We find that two-point functions decay as a power-law with exponent equal to one. Furthermore, we consider the case that the spin variables transform in the fundamental representation of SO(N), leading to a gapless system, and find that the effective central charge obtained from the entanglement entropy scales as lnN, reflecting the number of local degrees of freedom. We also determine the dependence of this central charge on the parameters specifying the bulk tiling. Moreover, we obtain an analytical expression for the mutual information, according to which there is no phase transition at any finite value of the distance between the two intervals involved.

• Okunishi et al., Holographic Analysis of Boundary Correlation Functions for the Hyperbolic-Lattice Ising Model
  2024, 093A02 (2024) [Crossref]
• Basteiro et al., Entanglement in Interacting Majorana Chains and Transitions of von Neumann Algebras
  Phys. Rev. Lett. 132, 161604 (2024) [Crossref]
• Chen et al., Anderson Localization Transition in Disordered Hyperbolic Lattices
  Phys. Rev. Lett. 133, 066101 (2024) [Crossref]
• Shankar et al., Hyperbolic Lattices and Two-Dimensional Yang-Mills Theory
  Phys. Rev. Lett. 133, 146601 (2024) [Crossref]
• Dey et al., Simulating Holographic Conformal Field Theories on Hyperbolic Lattices
  Phys. Rev. Lett. 133, 061603 (2024) [Crossref]