Phase diagram of the XXZ chain with next-nearest-neighbor interactions

Abstract

We calculate the quantum phase diagram of the {\it XXZ} chain with nearest-neighbor (NN) $J_1$ and next-NN exchange $J_2$ with anisotropies ${\Delta }_1$ and ${\Delta }_2$ respectively. In particular we consider the case ${\Delta }_1=-{\Delta }_2$ to interpolate between the {\it XX} chain () and the isotropic model with ferromagnetic $J_2$. For , a ferromagnetic and two antiferromagnetic phases exist. For $|{\Delta }_i|<1$, 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 ${\Delta }_1={\Delta }_2=1$ suggest that a small gap is present.

10 pages, 4 psfigures

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