Classical spin liquids from frustrated Ising models in hyperbolic space

Abstract

Antiferromagnetic Ising models on frustrated lattices can realize classical spin liquids, with highly degenerate ground states and, possibly, fractionalized excitations and emergent gauge fields. Motivated by the recent interest in many-body system in negatively curved space, we study hyperbolic frustrated Ising models. Specifically, we consider nearest-neighbor Ising models on tesselations with odd-length loops in two-dimensional hyperbolic space. For finite systems with open boundaries we determine the ground-state degeneracy exactly, and we perform extensive finite-temperature Monte-Carlo simulations to obtain thermodynamic data as well as correlation functions. We show that the shape of the boundary, constituting an extensive part of the system, can be used to control low-energy states: Depending on the boundary, we find ordered or disordered ground states. Our results demonstrate how geometric frustration acts in curved space to produce classical spin liquids.

References in corpus (28)

• Quantum Spin Liquids
• Spin Ice State in Frustrated Magnetic Pyrochlore Materials
• Magnetic Monopoles in Spin Ice
• A Field Guide to Spin Liquids
• Bekenstein-Hawking Entropy and Strange Metals
• Crystallography of Hyperbolic Lattices
• Hyperbolic band theory
• Hyperbolic and Semi-Hyperbolic Surface Codes for Quantum Storage
• Band theory and boundary modes of high-dimensional representations of infinite hyperbolic lattices
• Lattice Setup for Quantum Field Theory in AdS${}_2$
• Conformal Quasicrystals and Holography
• Corner Transfer Matrix Renormalization Group Method Applied to the Ising Model on the Hyperbolic Plane
• Ising model on hyperbolic lattice studied by corner transfer matrix renormalization group method
• Towards Explicit Discrete Holography: Aperiodic Spin Chains from Hyperbolic Tilings
• Simulating Holographic Conformal Field Theories on Hyperbolic Lattices
• Critical properties of the Ising model in hyperbolic space
• Curvature-induced frustration in the $XY$ model on hyperbolic surfaces
• Modular discretization of the AdS2/CFT1 Holography
• Converging Periodic Boundary Conditions and Detection of Topological Gaps on Regular Hyperbolic Tessellations
• Weak correlation effects in the Ising model on triangular-tiled hyperbolic lattices
• Tricritical point of J1-J2 Ising model on hyperbolic lattice
• Aperiodic spin chains at the boundary of hyperbolic tilings
• The Random-Bond Ising Model and its dual in Hyperbolic Spaces
• Hyperbolic Spin Liquids
• Critical Phenomena in Hyperbolic Space
• Chiral Gapless Spin Liquid in Hyperbolic Space
• Hubbard and Heisenberg models on hyperbolic lattices: Metal-insulator transitions, global antiferromagnetism, and enhanced boundary fluctuations
• Discrete JT gravity as an Ising model