Energy Scale Deformation on Regular Polyhedra

TL;DR

This paper investigates how energy scale deformation affects the ground states of the S=1/2 antiferromagnetic Heisenberg model on various polyhedral clusters, revealing stability in some and potential for generalization of sine-square deformation.

Contribution

It introduces a study of energy scale deformation on polyhedra, extending the concept of sine-square deformation to higher-dimensional structures.

Findings

Perturbations do not affect ground states on tetrahedral, octahedral, and cubic clusters when small.

Ground states on icosahedral and dodecahedral clusters are robust unless perturbations cause discontinuous changes.

Results suggest a possible generalization of sine-square deformation in higher dimensions.

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.