Antiferromagnetic Heisenberg Linear Chain—a Renormalized Linked Cluster Expansion

Abstract

A renormalized linked cluster expansion is carried out for a one-dimensional Heisenberg antiferromagnetic model. The temperature dependence of the energy and specific heat, and the field dependence of the magnetization and susceptibility at absolute zero, are calculated to second order. In particular, the ground-state energy $\frac{E_G}{\mathrm{NJ}}=0.8702\mathrm{}$ is obtained, and a zero-temperature susceptibility $\frac{4J_{\chi }}{N{g}^2\mu _B^{}{}_{}{}^2}=0.2590\mathrm{}$. The field dependence of the magnetization and entropy at several temperatures are calculated to first order. The present theory compares satisfactorily with experiments on Cu${\left(\mathrm{N}{\mathrm{H}}_3\right)}_4$S${\mathrm{O}}_4$·${\mathrm{H}}_2$O.