Magnons in a two dimensional transverse field XXZ model

TL;DR

This study investigates the magnon excitations and phase diagram of a 2D XXZ model under a transverse magnetic field using spin wave theory and quantum Monte Carlo simulations, revealing ground state properties, symmetry restoration, and magnon band crossings.

Contribution

The paper combines analytical spin wave theory with large-scale quantum Monte Carlo simulations to analyze magnon behavior and phase transitions in the 2D XXZ model under transverse fields, providing new insights into symmetry and excitation spectra.

Findings

Identification of an unentangled factorized ground state at intermediate fields.

Observation of Goldstone modes in field-free and saturated regimes.

Discovery of magnon degeneracy and band crossing due to symmetry restoration.

Abstract

The XXZ model on a square lattice in the presence of a transverse magnetic field is studied within the spin wave theory to investigate the resulting canted antiferromagnet. The small and large field regimes are probed separately both for easy-axis and easy-plane scenarios which reveal an unentangled factorized ground state at an intermediate value of the field. Goldstone modes are obtained for the field-free $XY$ antiferromagnet as well as for the isotropic antiferromagnet with field up to its saturation value. Moreover, for an easy-plane anisotropy, we find that there exists a non-zero field, where magnon degeneracy appears as a result of restoration of an U(1) sublattice symmetry and that, across that field, there occurs a magnon band crossing. For completeness, we then obtain the system phase diagram for $S=1/2$ via large scale quantum Monte Carlo simulations using the stochastic series expansion technique. Our numerical method is based on a quantization of spin along the direction of the applied magnetic field and does not suffer from a sign-problem, unlike comparable algorithms based on a spin quantization along the axis of anisotropy. With this formalism, we are also able to obtain powder averages of the transverse and longitudinal magnetizations, which may be useful for understanding experimental measurements on polycrystalline samples.