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arXiv:cond-mat/0105119 · Physical review. B, Condensed matter

Phase diagram of theXXZchain with next-nearest-neighbor interactions

Rolando D. Somma, Armando A. Aligia

Published Jun 19, 2001• 52 citations
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Abstract

We calculate the quantum phase diagram of an XXZ chain with nearest-neighbor (NN) ${J}_{1}$ and next-NN exchange ${J}_{2}$ with anisotropies ${\ensuremath{\Delta}}_{1}$ and ${\ensuremath{\Delta}}_{2},$ respectively. In particular we consider the case ${\ensuremath{\Delta}}_{1}=\ensuremath{-}{\ensuremath{\Delta}}_{2},$ to interpolate between the XX chain $({\ensuremath{\Delta}}_{i}=0)$ and the isotropic model with ferromagnetic phase ${J}_{2}.$ For ${\ensuremath{\Delta}}_{1}<\ensuremath{-}1,$ a ferromagnetic phase and two antiferromagnetic phases exist. For $|{\ensuremath{\Delta}}_{i}|<1,$ the boundary between the dimer and spin fluid phases is determined by the method of crossing of excitation spectra. For large ${J}_{2}{/J}_{1},$ this method seems to indicate the existence of a second spin fluid critical phase. However, an analysis of the spin stiffness and magnetic susceptibility for ${\ensuremath{\Delta}}_{1}={\ensuremath{\Delta}}_{2}=1$ suggests that a small gap is present.

DOI
10.1103/physrevb.64.024410

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