Convergent expansions for properties of the Heisenberg model for CaV$_4$O$_9$

TL;DR

This paper uses high-order perturbation and high-temperature expansions to analyze the magnetic properties of the CaV$_4$O$_9$ compound, providing insights into its exchange interactions and excitation spectrum.

Contribution

It applies convergent high-order perturbation and high-temperature expansions to the Heisenberg model for CaV$_4$O$_9$, offering detailed quantitative analysis of its magnetic properties.

Findings

Nearest-neighbor exchange ~200K

Second-neighbor exchange ~100K

Magnetic properties well described by the model

Abstract

We have carried out a wide range of calculations for the $S=1/2$ Heisenberg model with nearest- and second-neighbor interactions on a two-dimensional lattice which describes the geometry of the vanadium ions in the spin-gap system CaV$_4$O$_9$. The methods used were convergent high-order perturbation expansions (``Ising'' and ``Plaquette'' expansions at $T=0$, as well as high-temperature expansions) for quantities such as the uniform susceptibility, sublattice magnetization, and triplet elementary excitation spectrum. Comparison with the data for CaV$_4$O$_9$ indicates that its magnetic properties are well described by nearest-neighbor exchange of about 200K in conjunction with second-neighbor exchange of about 100K.