Hyperbolic Deformation Applied to S = 1 Spin Chains - Scaling Relation in Excitation Energy -

TL;DR

This paper studies how hyperbolic deformation affects excitation energies in S=1 spin chains, providing a scaling relation to estimate excitation gaps in the uniform limit using finite size scaling.

Contribution

It introduces a hyperbolic deformation approach to analyze excitation energies and derives a scaling relation to estimate gaps in uniform spin chains.

Findings

Elementary excitations are well described by a quasiparticle hopping model.

A finite size scaling method estimates the excitation gap in the uniform limit.

Hyperbolic deformation provides a new perspective on excitation energy analysis.

Abstract

We investigate excitation energies of hyperbolically deformed S = 1 spin chains, which are specified by the local energy scale f_j^{~} = \cosh j \lambda, where j is the lattice index and \lambda is the deformation parameter. The elementary excitation is well described by a quasiparticle hopping model, which is also expressed in the form of hyperbolic deformation. It is possible to estimate the excitation gap \Delta in the uniform limit \lambda \rightarrow 0, by means of a finite size scaling with respect to the system size N and the deformation parameter \lambda.