Functional integral theories of low-dimensional quantum Heisenberg models

Abstract

We investigate the low-temperature properties of the quantum Heisenberg models, both ferromagnetic and antiferromagnetic, in one and two dimensions. We study two different large-N formulations, using Schwinger bosons and S=(1/2 fermions, and solve for their low-order thermodynamic properties. Comparison with exact solutions in one dimension demonstrates the applicability of this expansion to the physical models at N=2. For the square lattice, we find at the mean-field level a low-temperature correlation length which behaves as \ensuremath{\xi}\ensuremath{\propto}exp(A/T), where A asymptotically approaches 2\ensuremath{\pi}${S}^{2}$ for large spin S, but ${A}_{S=1/2}$\ensuremath{\simeq}1.16 and ${A}_{S=1}$\ensuremath{\simeq}5.46. We mention the relevance of our results to recent experiments in ${\mathrm{La}}_{2}$${\mathrm{CuO}}_{4}$.