Direct Calculation of Spin-Stiffness for Spin-1/2 Heisenberg Models

TL;DR

This paper introduces a method for directly calculating the spin-stiffness in frustrated spin-1/2 Heisenberg models using exact diagonalizations with twisted boundary conditions, providing new insights into their properties.

Contribution

It presents the first direct calculation of spin-stiffness for frustrated spin-1/2 Heisenberg models, including finite-size extrapolation to the thermodynamic limit.

Findings

Spin-stiffness for unfrustrated planar antiferromagnet is 0.14±0.01.

Method applies to frustrated models in 1D and 2D.

Discussion of linear-response theory and moment sum-rule.

Abstract

The spin-stiffness of frustrated spin-1/2 Heisenberg models in one and two dimensions is computed for the first time by exact diagonalizations on small clusters that implement spin-dependent twisted boundary conditions. Finite-size extrapolation to the thermodynamic limit yields a value of $0.14\pm 0.01$ for the spin-stiffness of the unfrustrated planar antiferromagnet. We also present a general discussion of the linear-response theory for spin-twists, which ultimately leads to the moment sum-rule.