Spin-Wave-Spin-Wave Interaction and the Thermodynamics of the Heisenberg Spin Chain

TL;DR

This paper derives the low-temperature free energy of the quantum Heisenberg ferromagnetic chain considering two-spin-wave interactions, revealing a linear temperature dependence of the exchange constant, beyond perturbation theory.

Contribution

It introduces a non-perturbative two-particle approximation that accounts for both bound and scattering states in the spin-wave interactions of the Heisenberg chain.

Findings

Main temperature renormalization of exchange constant is linear in T

Inclusion of scattering states alters thermodynamic predictions

Results go beyond traditional perturbation theory

Abstract

The low-temperature free energy of the spin S quantum Heisenberg ferromagnetic chain in a strong magnetic field is obtained in a two-particle approximation by using exact solution of two-spin-wave problem. The result is beyond the perturbation theory because it incorporates the both bound and scattering state contributions, and the scattering effect is essential as well as the bound state one. In particular the main temperature renormalization of an exchange constant is found to be linear in temperature instead $T^{3/2}$ corresponded to the perturbation theory result.