Phase diagrams of XXZ model on depleted square lattice

TL;DR

This study explores the phase diagram of the spin-1/2 XXZ model on a depleted square lattice using QMC simulations and mean field theory, revealing novel magnetic phases and phase transitions influenced by lattice depletion and magnetic field.

Contribution

It provides new insights into the ground state phases and phase transitions of the depleted XXZ model, combining numerical and analytical methods for the first time.

Findings

Identification of antiferromagnetic and ferromagnetic phases on depleted lattice

Agreement between QMC and mean field theory on phase interpretation

Observation of Kosterlitz-Thouless and second order phase transitions

Abstract

Using quantum Monte Carlo (QMC) simulations and a mean field (MF) 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 $m_{z}=\pm 1/6$ 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.