A note on the high temperature expansion of the density matrix for the isotropic Heisenberg chain

Abstract

G\"ohmann, Kl\"umper and Seel derived the multiple integral formula of the density matrix of the $XXZ$ Heisenberg chain at finite temperatures. We have applied the high temperature expansion (HTE) method to isotropic case of their formula in a finite magnetic field and obtained coefficients for several short-range correlation functions. For example, we have succeeded to obtain the coefficients of the HTE of the 3rd neighbor correlation function $<\sigma_{j}^{z}\sigma_{j+3}^{z}>$ for zero magnetic field up to the order of 25. These results expand our previous results on the emptiness formation probability [Z.Tsuboi, M.Shiroishi, J. Phys.A: Math. Gen. 38(2005) L363; cond-mat/0502569] to more general correlation functions.