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Bulletin of the American Physical Society

Spectrum, symmetries, and dynamics of Heisenberg spin-1/2 chains

Kira Joel, Davida Kollmar, Léa Ferreira dos Santos

Published Mar 18, 2013• 0 citations
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We investigate the formation of a spin gap in one-dimensional models characterized by groups with hidden dynamical symmetries. A family of two-parametric models of isotropic and anisotropic spin-rotator chains (SRC's) characterized by $\mathrm{SU}(2)\ifmmode\times\else\texttimes\fi{}\mathrm{SU}(2)$ and $\mathrm{SO}(2)\ifmmode\times\else\texttimes\fi{}\mathrm{SO}(2)\ifmmode\times\else\texttimes\fi{}{\mathrm{Z}}_{2}\ifmmode\times\else\texttimes\fi{}{\mathrm{Z}}_{2}$ symmetries is introduced to describe the transition from SU(2) to SO(4) antiferromagnetic Heisenberg chains. The excitation spectrum is studied with the use of the Jordan-Wigner transformation generalized for o4{o}_{4}o4​ algebra and by means of the 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∕32∕32∕3, in contrast to dimension 1 in the conventional Haldane problem.