Finite-temperature perturbation theory for quasi-one-dimensional spin-12Heisenberg antiferromagnets

We develop a finite-temperature perturbation theory for quasi-one-dimensional quantum spin systems, in the manner suggested by Schulz in Phys. Rev. Lett. 77, 2790 (1996) and use this formalism to study their dynamical response. The corrections to the random-phase approximation formula for the dynamical magnetic susceptibility obtained with this method involve multipoint correlation functions of the one-dimensional theory on which the random-phase approximation expansion is built. This “anisotropic” perturbation theory takes the form of a systematic high-temperature expansion. This formalism is first applied to the estimation of the Néel temperature of $S=1/2\mathrm{}$ anisotropic cubic lattice Heisenberg antiferromagnets. It is then applied to the compound ${\mathrm{Cs}}_2{\mathrm{CuCl}}_4,$ a frustrated $S=1/2\mathrm{}$ antiferromagnet with a Dzyaloshinskii-Moriya spin anisotropy. Using the next leading order to the random-phase approximation, we determine the improved values for the critical temperature and incommensurability. Despite the nonuniversal character of these quantities, the calculated values compare remarkably well with the experimental values for both compounds.