Non-linear bond-operator theory and 1/d expansion for coupled-dimer magnets I: Paramagnetic phase

TL;DR

This paper develops a systematic 1/d expansion using bond-operator techniques to analyze coupled-dimer Heisenberg magnets in the paramagnetic phase, providing analytical results that compare well with numerical data.

Contribution

It introduces a novel 1/d expansion method for coupled-dimer magnets, extending bond-operator theory to arbitrary dimensions and analyzing the paramagnetic phase near quantum criticality.

Findings

Calculated static and dynamic observables at zero temperature.

Compared analytical results with numerical data for d=2.

Connected the approach with previous bond-operator refinements.

Abstract

For coupled-dimer Heisenberg magnets, a paradigm of magnetic quantum phase transitions, we develop a systematic expansion in 1/d, the inverse number of space dimensions. The expansion employs a formulation of the bond-operator technique and is based on the observation that a suitably chosen product-state wavefunction yields exact zero-temperature expectation values of local observables in the d->infty limit, with corrections vanishing as 1/d. We demonstrate the approach for a model of dimers on a hypercubic lattice, which generalizes the square-lattice bilayer Heisenberg model to arbitrary d. In this paper, we use the 1/d expansion to calculate static and dynamic observables at zero temperature in the paramagnetic singlet phase, up to the quantum phase transition, and compare the results with numerical data available for d=2. Contact is also made with previously proposed refinements of bond-operator theory as well as with a perturbative expansion in the inter-dimer coupling. In a companion paper, the present 1/d expansion will be extended to the ordered phase, where it is shown to consistently describe the entire phase diagram including the quantum critical point.