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arXiv:0705.2990 · Physical Review B

Dimer phases in quantum antiferromagnets with orbital degeneracy

George Jackeli, Dmitri A. Ivanov

Published Oct 22, 2007• 28 citations
arXivHTMLPDF

Abstract

We study and solve the ground-state problem of a microscopic model for a family of orbitally degenerate quantum magnets. The orbital degrees of freedom are assumed to have a directional character and are represented by static Potts-like variables. In the limit of vanishing Hund's coupling, the ground-state manifold of such a model is spanned by the hard-core dimer (spin singlet) coverings of the lattice. The extensive degeneracy of dimer coverings is lifted at a finite Hund's coupling through an order--out-of-disorder mechanism by virtual triplet excitations. The relevance of our results to several experimentally studied systems is discussed.

DOI
10.1103/physrevb.76.132407

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We extend to magnetically ordered phases a recently developed expansion in 1/d1/d1/d for coupled-dimer Heisenberg magnets, where ddd is the number of space dimensions. This extension utilizes generalized bond operators describing spin excitations on top of a reference state involving triplet condensates. We explicitly consider a model of dimers on a hypercubic lattice which displays, in addition to the paramagnetic singlet phase, a collinear antiferromagnetic phase for which we calculate static and dynamic observables at zero temperature. In particular, we show that the 1/d1/d1/d expansion smoothly connects the paramagnetic and antiferromagnetic phases and produces sensible results at and near the quantum phase transition point. Among others, we determine the dispersion and spectral-weight distribution of the amplitude (i.e., Higgs) mode of the ordered phase. In the limit of vanishing intradimer coupling, we connect our approach to spin-wave theory.
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