Phase diagrams of theXXZmodel on a depleted square lattice

Abstract

Using quantum Monte Carlo (QMC) simulations and a mean field theory, we investigate the spin-1/2 $XXZ$ model with nearest-neighbor interactions on a periodic depleted square lattice. In particular, we present results for 1/4 depleted lattice in an applied magnetic field and investigate the effect of depletion on the ground state. The ground state phase diagram is found to include an antiferromagnetic (AF) phase of magnetization ${m}_{z}=\ifmmode\pm\else\textpm\fi{}1/6$ and an in-plane ferromagnetic (FM) phase with finite spin stiffness. The agreement between the QMC simulations and the mean-field theory based on resonating trimers suggests the AF phase and in-plane FM phase can be interpreted as a Mott insulator and superfluid of trimer states, respectively. While the thermal transitions of the in-plane FM phase are well described by the Kosterlitz-Thouless transition, the quantum-phase transition from the AF phase to in-plane FM phase undergo a direct second-order insulator-superfluid transition upon increasing magnetic field.