Mean Field theory of the spin-Peierls transition

TL;DR

This paper applies mean field, bosonization, and Bethe Ansatz techniques to analyze the thermodynamics and phase transition of a spin-1/2 chain undergoing a spin-Peierls transition, providing detailed predictions of physical properties.

Contribution

It introduces a comprehensive mean field approach combined with bosonization and Bethe Ansatz to quantitatively study the spin-Peierls transition in one dimension.

Findings

Predicted specific heat and magnetic susceptibility across the dimerized phase.

Analyzed the effects of small magnetic fields on the transition.

Derived parameters for the Landau-Ginzburg theory near criticality.

Abstract

We revisit the problem of the spin-Peierls instability in a one dimensional spin-1/2 chain coupled to phonons. The phonons are treated within the mean field approximation. We use bosonization techniques to describe the gapped spin chain and then use the Thermodynamic Bethe Ansatz to obtain quantitative results for the thermodynamics of the spin-Peierls system in a whole range of temperature. This allows us to predict the behavior of the specific heat and the magnetic susceptibility in the entire dimerized phase. We study the effect of small magnetic fields on the transition. Moreover, we obtain the parameters of the Landau-Ginzburg theory describing this continuous phase transition near the critical point.