Complete Boundary Phase Diagram of the Spin-
21 XXZ Chain with Boundary Fields in the Anti-Ferromagnetic Gapped Regime
We consider the spin
21 XXZ chain with diagonal boundary fields and solve it exactly using Bethe ansatz in the gapped anti-ferromagnetic regime and obtain the complete phase boundary diagram. Depending on the values of the boundary fields, the system exhibits several phases which can be categorized based on the ground state exhibited by the system and also based on the number of bound states localized at the boundaries. We show that the Hilbert space is comprised of a certain number of towers whose number depends on the number of boundary bound states exhibited by the system. The system undergoes boundary phase transitions when boundary fields are varied across certain critical values. There exist two types of phase transitions. In the first type the ground state of the system undergoes a change. In the second type, named the `Eigenstate phase transition', the number of towers of the Hilbert space changes, which is again associated with the change in the number of boundary bound states exhibited by the system. We use the DMRG and exact diagonalization techniques to probe the signature of the Eigenstate phase transition and the ground state phase transition by analyzing the spin profiles in each eigenstate.
Phase transitions of the spin-1
XXZ chain with a single-ion anisotropy in a staggered magnetic field are studied. We obtain interesting phase diagrams consisting of ferromagnetic, partially ferromagnetic,
XY, antiferromagnetic (AF) and large-
D phases. By using the twist-boundary-condition method, a Gaussian critical line is found between the AF phase and the large-
D phase. A multicritical point lies among the
XY, AF and large-
D phases. An Ashkin-Teller type of bifurcation does not appear.
We calculate the quantum phase diagram of an XXZ chain with nearest-neighbor (NN)
J1 and next-NN exchange
J2 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
J2. 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
J2/J1, 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.