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 $Δ_{1}$ and $Δ_{2}$ respectively. In particular we consider the case $Δ_{1}=-Δ_{2}$ to interpolate between the {\it XX} chain ($% Δ_{i}=0$) and the isotropic model with ferromagnetic $J_{2}$. For $% Δ_{1}<-1$, a ferromagnetic and two antiferromagnetic phases exist. For $| Δ_{i}| <1$, 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 $Δ_{1}=Δ_{2}=1$ suggest that a small gap is present.