Optical Absorption of CuO$_3$ antiferromagnetic chains at finite temperatures

TL;DR

This paper combines numerical and analytical methods to study the optical absorption spectra of CuO$_3$ chains at finite temperatures, providing predictions consistent with experiments and advancing understanding of 1D antiferromagnetic systems.

Contribution

It introduces a finite temperature analytical ansatz for the dynamical energy correlation function and applies it to predict optical absorption spectra in quasi 1D antiferromagnetic compounds.

Findings

Good agreement with experimental optical absorption data at low temperatures

Provides a finite temperature prediction for the dynamics of the Heisenberg model

Develops a novel analytical ansatz validated by quantum Monte Carlo simulations

Abstract

We use a high-statistic quantum Monte Carlo and Maximum Entropy regularization method to compute the dynamical energy correlation function (DECF) of the one-dimensional (1D) $S=1/2$ antiferromagnetic Heisenberg model at finite temperatures. We also present a finite temperature analytical ansatz for the DECF which is in very good agreement with the numerical data in all the considered temperature range. From these results, and from a finite temperature generalisation of the mechanism proposed by Lorenzana and Sawatsky [Phys. Rev. Lett. {\bf 74}, 1867 (1995)], we compute the line shape for the optical absorption spectra of multimagnon excitations assisted by phonons for quasi 1D compounds. The line shape has two contributions analogous to the Stokes and anti-Stokes process of Raman scattering. Our low temperature data is in good agreement with optical absorption experiments of CuO$_3$ chains in Sr$_2$CuO$_3$. Our finite temperature results provide a non trivial prediction on the dynamics of the Heisenberg model at finite temperatures that is easy to verify experimentally.