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

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 (${J}_{1}$) and next-to-nearest neighbors (${J}_{2}$). In zero field, the system displays a large degeneracy of the ground state, which is exponential in the system size (for ${J}_{1}={J}_{2}$) or in the system's linear dimensions (for ${J}_{2}>{J}_{1}$). 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 nonlinear fluctuations are accounted for, in agreement with existing results for the isotropic case ${J}_{1}={J}_{2}$. Moreover, spin-wave theory shows sizable regions of instability, which are further candidates for quantum-disordered behavior.