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arXiv · 1202.1462

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

Louis-Paul Henry·Peter C. W. Holdsworth·Frédéric Mila·Tommaso Roscilde
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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.

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Louis-Paul Henry, Peter C. W. Holdsworth, Frédéric Mila, Tommaso Roscilde. 2012-02-07. Spin-wave analysis of the transverse-field Ising model on the checkerboard lattice. https://doi.org/10.1103/physrevb.85.134427

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