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.

6 pages, 10 figures

References in corpus (24)

• Highly Frustrated Magnetic Clusters: The kagome on a sphere
• Connecting distant ends of one-dimensional critical systems by a sine-square deformation
• Periodically, Quasi-periodically, and Randomly Driven Conformal Field Theories: Part I
• Floquet conformal field theories with generally deformed Hamiltonians
• Exact ground state of the sine-square deformed XY spin chain
• 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
• The fine structure of heating in a quasiperiodically driven critical quantum system
• Classification of $S{L}_2$ deformed Floquet Conformal Field Theories
• Infinite circumference limit of conformal field theory
• 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
• 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
• Hyperbolic Deformation on Quantum Lattice Hamiltonians
• Conformal Floquet dynamics with a continuous drive protocol
• The Real-Time Correlation Function of Floquet Conformal Fields
• Scaling Relation for Excitation Energy Under Hyperbolic Deformation
• 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