Analysis of quantum spin models on hyperbolic lattices and Bethe lattice

Abstract

The quantum XY, Heisenberg, and transverse field Ising models on hyperbolic lattices are studied by means of the Tensor Product Variational Formulation algorithm. The lattices are constructed by tessellation of congruent polygons with coordination number equal to four. The calculated ground-state energies of the XY and Heisenberg models and the phase transition magnetic field of the Ising model on the series of lattices are used to estimate the corresponding quantities of the respective models on the Bethe lattice. The hyperbolic lattice geometry induces the mean-field-like universality of the models. The ambition to obtain results on the non-Euclidean lattice geometries has been motivated by theoretical studies of the anti-de Sitter/conformal field theory correspondence.

14 pages, 6 figures, J. Phys. A: Math. Theor. (2016) in press

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• Variational optimization of tensor-network states with the honeycomb-lattice corner transfer matrix
• Critical line of the triangular Ising antiferromagnet in a field from a $C_3$-symmetric corner transfer matrix algorithm
• Corner transfer matrix renormalization group approach in the zoo of Archimedean lattices
• Free Energy Analysis of Spin Models on Hyperbolic Lattice Geometries
• Hyperbolic lattices and two-dimensional Yang-Mills theory
• Hyperbolic Spin Liquids
• Statistical Mechanics Approach to the Holographic Renormalization Group: Bethe Lattice Ising Model and p-adic AdS/CFT
• Hubbard and Heisenberg models on hyperbolic lattices: Metal-insulator transitions, global antiferromagnetism, and enhanced boundary fluctuations
• Absence of Weak Localization on Negative Curvature Surfaces
• Inner non-Hermitian skin effect on Bethe lattice
• Boundary-field-driven control of discontinuous phase transitions on hyperbolic lattices
• Efficient iPEPS Simulation on the Honeycomb Lattice via QR-based CTMRG
• Vertex Representation of Hyperbolic Tensor Networks
• Flat bands and band touching from real-space topology in hyperbolic lattices
• Discrete holography and density of states in the crossover from hyperbolic to Euclidean lattices
• Tensor-Network study of Ising model on infinite hyperbolic dodecahedral lattice