Hydrodynamic relation in 2D Heisenberg antiferromagnet in a field

TL;DR

This paper investigates the non-analytic dependence of spin-stiffness on magnetic field in a 2D Heisenberg antiferromagnet and shows the hydrodynamic relation remains valid due to mutual cancellations, providing explicit calculations across all fields.

Contribution

It provides explicit expressions for field-dependent spin stiffness and magnon velocity in a 2D antiferromagnet, confirming the hydrodynamic relation holds despite non-analytic behavior.

Findings

Hydrodynamic relation remains valid despite non-analytic field dependence.

Explicit expressions for spin stiffness and magnon velocity are derived.

Mutual cancellation of non-analytic terms ensures consistency of hydrodynamic relation.

Abstract

The spin-stiffness \rho_s of a 2D Heisenberg antiferromagnet depends non-analytically on external magnetic field. We demonstrate that the hydrodynamic relation between \rho_s, the uniform susceptibility \chi, and the spin-wave velocity $c$ is not violated by such a behavior because similar non-analytic terms from all three quantities mutually cancel out. In this work, explicit expressions for the field-dependent spin stiffness and for the magnon velocity of the 2D square lattice antiferromagnet are obtained by direct calculation to order 1/S and in the whole range of magnetic fields.