Spin Stiffness in the Hubbard model

TL;DR

This paper investigates the spin stiffness in the Hubbard model, deriving new expressions that clarify its physical interpretation and explore its relation to superconductivity and gauge invariance.

Contribution

It introduces new formulas for the spin stiffness in the Hubbard model, linking it to thermodynamic and hydrodynamic properties, and discusses its broader physical implications.

Findings

Derived new expressions for spin stiffness $ ho_s$

Established connection between $ ho_s$ and superconducting weight

Discussed gauge invariance in the context of spin stiffness

Abstract

The spin stiffness $\rho_{\rm s}$ of the repulsive Hubbard model that occurs in the hydrodynamic theory of antiferromagnetic spin waves is shown to be the same as the thermodynamically defined stiffness involved in twisting the order parameter. New expressions for $\rho_{\rm s}$ are derived, which enable easier interpretation, and connections with superconducting weight and gauge invariance are discussed.