Quantum triangular ice in the easy-axis ferromagnetic phase

TL;DR

This paper uses spin wave theory to analyze the ground state and excitation properties of a $Z_2$-invariant quantum XXZ model on a triangular lattice, revealing a gapped ferromagnetic phase with unique spectral features.

Contribution

It provides the first detailed spin wave analysis of the $Z_2$-invariant quantum XXZ model on a triangular lattice, highlighting the gapped spectrum and symmetry-breaking effects.

Findings

Quantum fluctuations are suppressed, validating linear spin wave theory.

The system exhibits a gapped excitation spectrum with a maxon dispersion at zero momentum.

Unusual peaks in the dynamical structure factors occur at specific wave vectors.

Abstract

We use spin wave theory to investigate the ground state properties of the $Z_2$-invariant quantum XXZ model on the triangular lattice in the ferromagnetic phase. The Hamiltonian comprises nearest and next-nearest-neighbour Ising couplings, external magnetic fields, and a $Z_2$-invariant ferromagnetic coupling. We show that quantum fluctuations are suppressed in this system, hence linear spin wave theory gives reasonable estimates of the ground state thermodynamic properties. Our results show that, at half-filling (zero magnetic fields), the spontaneous breaking of $Z_2$ symmetry leads to a ferromagnetic phase whose energy spectrum is gapped at all excitations with a maxon dispersion at $\mathbf{k}=0$. This is in sharp contrast to rotational invariant systems with a vanishing phonon dispersion. We show that the $\mathbf{k}=0$ mode enhances the estimated values of the thermodynamic quantities. We obtain the trends of the particle density and the condensate fraction. The density of states and the dynamical structure factors exhibit fascinating peaks at unusual wave vectors, which should be of interest.