Energy Scale Deformation on Regular Polyhedra

Abstract

A variant of energy scale deformation is considered for the S = 1/2 antiferromagnetic Heisenberg model on polyhedra. The deformation is induced by the perturbations to the uniform Hamiltonian, whose coefficients are determined by the bond coordinates. On the tetrahedral, octahedral, and cubic clusters, the perturbative terms do not affect the ground state of the uniform Hamiltonian when they are sufficiently small. On the other hand, for the icosahedral and dodecahedral clusters, it is numerically confirmed that the ground state of the uniform Hamiltonian is almost insensitive to the perturbations unless they lead to a discontinuous change in the ground state. The obtained results suggest the existence of a generalization of sine-square deformation in higher dimensions.

arXiv comment6 pages, 10 figures

References in corpus (55)

• Controlling frustrated liquids and solids with an applied field in a kagome Heisenberg antiferromagnet
• Effects of frustration on magnetic molecules: a survey from Olivier Kahn till today
• Independent magnon states on magnetic polytopes
• The Antiferromagnetic Heisenberg Model on Clusters with Icosahedral Symmetry
• Magnetic Properties of Undoped $C_{60}$
• Highly Frustrated Magnetic Clusters: The kagome on a sphere
• Evolution operators in conformal field theories and conformal mappings: the entanglement Hamiltonian, the sine-square deformation, and others
• Spherical Deformation for One-dimensional Quantum Systems
• Connecting distant ends of one-dimensional critical systems by a sine-square deformation
• Quantum dynamics in sine-square deformed conformal field theory: Quench from uniform to non-uniform CFTs
• Periodically, Quasi-periodically, and Randomly Driven Conformal Field Theories: Part I
• Sine-square deformation of solvable spin chains and conformal field theories
• Smooth Boundary Conditions For Quantum Lattice Systems
• Emergent Black Hole Dynamics in Critical Floquet Systems
• Emergent Spatial Structure and Entanglement Localization in Floquet Conformal Field Theory
• Sine-square deformation of free fermion systems in one and higher dimensions
• Floquet conformal field theories with generally deformed Hamiltonians
• Boundary effects in the density-matrix renormalization group calculation
• Exact ground state of the sine-square deformed XY spin chain
• Sine-square deformation and Mobius quantization of two-dimensional conformal field theory
• Suppression of finite-size effects in one-dimensional correlated systems
• Enhanced magnetocaloric effect in a proximity of magnetization steps and jumps of spin-1/2 XXZ Heisenberg regular polyhedra
• Holographic Duals of Inhomogeneous Systems: The Rainbow Chain and the Sine-Square Deformation Model
• Dipolar quantization and the infinite circumference limit of two-dimensional conformal field theories
• The fine structure of heating in a quasiperiodically driven critical quantum system
• Infinite circumference limit of conformal field theory
• Classification of $S{L}_2$ deformed Floquet Conformal Field Theories
• Entanglement Hamiltonian of quantum critical chains and conformal field theories
• The $s=1/2$ Antiferromagnetic Heisenberg Model on Fullerene-Type Symmetry Clusters
• Large-scale numerical investigations of the antiferromagnetic Heisenberg icosidodecahedron
• Antiferromagnetic Heisenberg Model on the Icosahedron: Influence of Connectivity and the Transition from the Classical to the Quantum Limit
• Deterministic chaos and fractal entropy scaling in Floquet CFT
• Sine-Square Deformation and its Relevance to String Theory
• Magnetic susceptibility of quantum spin systems calculated by sine square deformation: one-dimensional, square lattice, and kagome lattice Heisenberg antiferromagnets
• Zero-energy states in conformal field theory with sine-square deformation
• Geometry and Complexity of Path Integrals in Inhomogeneous CFTs
• The antiferromagnetic $S=1/2$ Heisenberg model on the ${\text{C}}_{60}$ fullerene geometry
• Conformal Quantum Mechanics and Sine-Square Deformation
• Hyperbolic Deformation on Quantum Lattice Hamiltonians
• Conformal Floquet dynamics with a continuous drive protocol
• The Hubbard model with smooth boundary conditions
• Variational Hilbert space truncation approach to quantum Heisenberg antiferromagnets on frustrated clusters
• Correlations for the S=1/2 Antiferromagnet on a Truncated Tetrahedron
• Scaling Relation for Excitation Energy Under Hyperbolic Deformation
• Scale free property and edge state of Wilson's numerical renormalization group
• The Real-Time Correlation Function of Floquet Conformal Fields
• Time development of conformal field theories associated with $L_1$ and $L_{-1}$ operators
• Advanced quantum methods for the largest magnetic molecules
• Sine-square deformation and supersymmetric quantum mechanics
• Ground state phase diagram of twisted three-leg spin tube in magnetic field
• Discontinuous quantum and classical magnetic response of the pentakis dodecahedron
• Wilson-like real-space renormalization group and low-energy effective spectrum of the XXZ chain in the critical regime
• Analysis for Lorentzian conformal field theories through sine-square deformation
• Closed string symmetries in open string field theory: tachyon vacuum as sine-square deformation
• Hyperbolic Deformation Applied to S = 1 Spin Chains - Scaling Relation in Excitation Energy -