Thermal Bethe-Ansatz Method for the One-Dimensional Heisenberg Model

徹 高麗

Tohru Koma

S.-J. Gu, Nuno M. R. Peres, You‐Quan Li

Tohru Koma

A new method is proposed for calculating the free energy of the one-dimensional spin-1/2 XXZ Heisenberg model. The partition function is written in terms of the transfer matrix for a two-dimensional Ising system, whose maximum eigenvalue is obtained by the Bethe-ansatz method leading to the free energy in the thermodynamic limit. This method uses no such assumption as the completeness of the Bethe states that has been proved only partially and yields better results than the previous methods do.

K. Nomura, Miki Yamada

We investigate the correlation length of the one-dimensional S=1/2 Heisenberg antiferromagnet by the thermal Bethe-ansatz method proposed by Koma. The numerical result shows that the correlation length diverges as \ensuremath{\xi}\ensuremath{\sim}${\mathit{T}}^{\mathrm{\ensuremath{-}}1}$ at low temperatures with logarithmic corrections. This logarithmic correction can be explained by conformal field theory.

J. Moens

The Bethe ansatz is used to analytically solve the Heisenberg model with nearest neighbour interactions for spin-1/2 particles in an one dimensional chain. Our goal is to find out if the Bethe ansatz can be extended to nearest and next nearest neighbour interactions and to gain insight into the system with exact diagonalization. We find that this cannot be done. Because of certain assumptions made in the Bethe ansatz, the method fails for next nearest neighbour interactions.