Spin-wave analysis of the transverse-field Ising model on the checkerboard lattice

TL;DR

This study uses linear spin wave theory to analyze the ground state properties of the transverse-field Ising model on the checkerboard lattice, revealing potential quantum-disordered phases due to degeneracy and instabilities.

Contribution

It applies spin wave analysis to a frustrated lattice model with variable couplings, highlighting the limitations of harmonic fluctuations and suggesting possible quantum-disordered ground states.

Findings

Degeneracy persists under quantum fluctuations at harmonic level.

Regions of instability indicate potential for quantum-disordered phases.

Quantum fluctuations do not lift degeneracy in the harmonic approximation.

Abstract

The ground state properties of the S=1/2 transverse-field Ising model on the checkerboard lattice are studied using linear spin wave theory. We consider the general case of different couplings between nearest neighbors (J1) and next-to-nearest neighbors (J2). In zero field the system displays a large degeneracy of the ground state, which is exponential in the system size (for J1=J2) or in the system's linear dimensions (for J2>J1). Quantum fluctuations induced by a transverse field are found to be unable to lift this degeneracy in favor of a classically ordered state at the harmonic level. This remarkable fact suggests that a quantum-disordered ground state can be instead promoted when non-linear fluctuations are accounted for, in agreement with existing results for the isotropic case J1=J2. Moreover spin-wave theory shows sizable regions of instability which are further candidates for quantum-disordered behavior.