Thermal Bethe Ansatz Study of Correlation Length of Spin-1/2 Heisenberg Ferromagnetic Chain

Abstract

The correlation length of the Heisenberg ferromagnetic chain with S =1/2 at sufficiently low temperatures (1/β J 10 -4 ) is obtained numerically (relative 10 -5 ) by the thermal Bethe Ansatz method developed recently by Koma. The numerical result shows directly that the critical exponent ν of the correlation length ξ defined as ξ∼ T -ν is ν=1 and ξ is expanded in \(\sqrt{T}\) near T =0. These results coincide with the new spin wave theory in case of no spontaneous magnetization developed by Takahashi quantitatively with the accuracy of 2×10 -3 % and 7×10 -2 % as for the first and second order terms of a low-temperature expansion respectively.