Eur. Phys. J. B 24, 77-84 (2001)
https://doi.org/10.1007/s100510170024

Finite size scaling of the spin stiffness of the antiferromagnetic S=1/2 XXZ chain

Laboratoire de Physique Quantique (UMR CNRS 5626) , Université Paul Sabatier, 31062 Toulouse, France

Corresponding author: ^a laflo@irsamc.ups-tlse.fr

Received: 23 May 2001
Revised: 26 July 2001
Published online: 15 November 2001

Abstract

We study the finite size scaling of the spin stiffness for the one-dimensional quantum antiferromagnet as a function of the anisotropy parameter Δ. Previous Bethe ansatz results allow a determination of the stiffness in the thermodynamic limit. The Bethe ansatz equations for finite systems are solvable even in the presence of twisted boundary conditions, a fact we exploit to determine the stiffness exactly for finite systems allowing for a complete determination of the finite size corrections. Relating the stiffness to thermodynamic quantities we calculate the temperature dependence of the susceptibility and its finite size corrections at T=0. A Luttinger liquid approach is used to study the finite size corrections using renormalization group techniques and the results are compared to the numerically exact results obtained using the Bethe ansatz equations. Both irrelevant and marginally irrelevant cases are considered.