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Acta Physica Sinica

PHASE DIGRAM OF SPIN 1/2 XXZ CHAIN

Zhijian Chen, Yumei Zhang, Xu Bo-wei, (1)上海交通大学物理系,上海200030; (2)上海交通大学物理系,上海200030中国科学院理论物理研究所,北京100080; (3)同济大学物理系,上海200092

Published Jan 1, 1995• 0 citations
Publisher

Abstract

By mapping the spin 1/2 XXZ quantum chain to sine-Gordon model, we have analyzed the phase diagram of sine-Gordon model using tke method of gaussian wave functional and taking the large momentum cutoff. We have obtained the mas-sless region which agrees with the exact solution quite well.
DOI
10.7498/aps.44.1697

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The (1+1)-dimensional sine-Gordon model is studied in the framework of the variational Gaussian wave functionals. The renormalized mass depends on two dimensionless parameters. In the phase diagram a first-order phase transition will replace the second-order phase transition for large bare mass. The spectrum of the two-particle states consists of a continuum of scattering states and the isolated values connected to the excitonlike bound states. The energy of the bound states and the phase shifts of the scattering states are explicitly calculated.
We consider here the XXZ spin chain perturbed by the operator ${\ensuremath{\sigma}}^{x}$ (``in a transverse field'') which is a lattice regularization of the sine-Gordon model. This can be shown using conformal perturbation theory. We calculate the mass ratios of particles which lie in a discrete part of the spectrum and obtain results in accord with the DHN formula and in disagreement with recent calculations in the literature based on the numerical Bethe ansatz and infinite momentum frame methods. We also analyze the short distance behavior of these states (UV or conformal limit). Our result for conformal dimension of the second breather state is different from that conjectured by Klassen and Melzer [Int. J. Mod. Phys. A 8, 4131 (1993)] and is consistent with this paper for other states.
The renormalization group equations for the sine-Gordon system with a short wave-length cutoff in two dimensions are derived by means of a momentum-shell recursion method. In a special limit they agree with the Kosterlitz renormalization group equations which describe the critical properties of the phase transitions of the two-dimensional (2-D) neutral Coulomb gas with single charges ±1 and of the 2-D isotropic X-Y model in the absence of an external field. The results, therefore, give rise to a possibility that certain classes of phase transitions in low dimensions can be described in a unified way with the sine-Gordon Hamiltonian.
From the identification of the easy-plane XXZ\mathrm{XXZ}XXZ spin chain as a ${\ensuremath{\beta}}^{2}>8\ensuremath{\pi}$ quantum sine-Gordon system, the nonlinear elementary excitations of the latter are identified as massless "twists" carrying the topological charge $\ifmmode\pm\else\textpm\fi{}\frac{{\ensuremath{\beta}}^{2}}{8\ensuremath{\pi}}$, and (depending on ${\ensuremath{\beta}}^{2}$) twist-antitwist bound states.