Free energy asymptotics of the quantum Heisenberg spin chain

Abstract

We consider the ferromagnetic quantum Heisenberg model in one dimension, for any spin $S\ge 1/2$. We give upper and lower bounds on the free energy, proving that at low temperature it is asymptotically equal to the one of an ideal Bose gas of magnons, as predicted by the spin-wave approximation. The trial state used in the upper bound yields an analogous estimate also in the case of two spatial dimensions, which is believed to be sharp at low temperature.

arXiv commentLaTeX, 22 pages; revised version

References in corpus (7)

• Fermi and Non-Fermi behavior in the anisotropic Multichannel Kondo Model -- Bethe Ansatz solution
• Proof of Aldous' spectral gap conjecture
• Lectures on the Bethe Ansatz
• Introduction to the thermodynamic Bethe ansatz
• Validity of the spin-wave approximation for the free energy of the Heisenberg ferromagnet
• The Free Energy of the Quantum Heisenberg Ferromagnet at Large Spin
• Validity of spin wave theory for the quantum Heisenberg model

Cited by in corpus (3)

• Correlation Energy of a Weakly Interacting Fermi Gas with Large Interaction Potential
• Bosonization of Fermionic Many-Body Dynamics
• Effective Dynamics of Interacting Fermions from Semiclassical Theory to the Random Phase Approximation