Spin Gap in Chains with Hidden Symmetries

TL;DR

This paper explores the formation of spin gaps in one-dimensional models with hidden symmetries, introducing new models and analyzing their excitation spectra to reveal unique scaling behaviors.

Contribution

It introduces a family of Spin-Rotator Chain models with hidden symmetries and studies their excitation spectra using advanced transformations, revealing novel spin gap characteristics.

Findings

Spin gap characterized by scaling dimension 2/3

Models interpolate between SU(2) and SO(4) chains

Hidden discrete symmetries influence the spin gap

Abstract

We investigate the formation of spin gap in one-dimensional models characterized by the groups with hidden dynamical symmetries. A family of two-parametric models of isotropic and anisotropic Spin-Rotator Chains characterized by SU(2)x SU(2) and SO(2)x SO(2)x Z_2 x Z_2 symmetries is introduced to describe the transition from SU(2) to SO(4) antiferromagnetic Heisenberg chain. The excitation spectrum is studied with the use of the Jordan-Wigner transformation generalized for o_4 algebra and by means of bosonization approach. Hidden discrete symmetries associated with invariance under various particle-hole transformations are discussed. We show that the spin gap in SRC Hamiltonians is characterized by the scaling dimension 2/3 in contrast to dimension 1 in conventional Haldane problem.