Finite-temperature perturbation theory for quasi-one-dimensional spin-1/2 Heisenberg antiferromagnets

摘要

We develop a finite-temperature perturbation theory for quasi-one-dimensionalquantum spin systems, in the manner suggested by H.J. Schulz (1996) and usethis formalism to study their dynamical response. The corrections to therandom-phase approximation formula for the dynamical magnetic susceptibilityobtained with this method involve multi-point correlation functions of theone-dimensional theory on which the random-phase approximation expansion isbuilt. This ``anisotropic'' perturbation theory takes the form of a systematichigh-temperature expansion. This formalism is first applied to the estimationof the N\'eel temperature of S=1/2 cubic lattice Heisenberg antiferromagnets.It is then applied to the compound Cs$_2$CuCl$_4$, a frustrated S=1/2antiferromagnet with a Dzyaloshinskii-Moriya anisotropy. Using the next leadingorder to the random-phase approximation, we determine the improved values forthe critical temperature and incommensurability. Despite the non-universalcharacter of these quantities, the calculated values are different by less thana few percent from the experimental values for both compounds.