Effects of Interactions on Dynamic Correlations of Hard-Core Bosons at Finite Temperatures

TL;DR

This paper studies how additional interactions influence the dynamic correlations of hard-core bosons at finite temperatures, especially in dimerized spin systems, by extending the Brückner approach to include NN and NNN interactions.

Contribution

It introduces an extended Brückner approach with a matrix Bethe-Salpeter equation to accurately account for additional interactions in finite-temperature correlation calculations.

Findings

Additional interactions lead to bound state formation.

Extended approach improves spectral function predictions.

Significant impact on neutron scattering rate calculations.

Abstract

We investigate how dynamic correlations of hard-core bosonic excitation at finite temperature are affected by additional interactions besides the hard-core repulsion which prevents them from occupying the same site. We focus especially on dimerized spin systems, where these additional interactions between the elementary excitations, triplons, lead to the formation of bound states, relevant for the correct description of scattering processes. In order to include these effects quantitatively we extend the previously developed Br\"uckner approach to include also nearest-neighbor (NN) and next-nearest neighbor (NNN) interactions correctly in a low-temperature expansion. This leads to the extension of the scalar Bethe-Salpeter equation to a matrix-valued equation. Exemplarily, we consider the Heisenberg spin ladder to illustrate the significance of the additional interactions on the spectral functions at finite temperature which are proportional to inelastic neutron scattering rates.