Quasi-particle interactions in frustrated Heisenberg chains

TL;DR

This paper uses matrix product states to analyze quasi-particle interactions in a frustrated spin chain, revealing detailed spectral features relevant for experimental neutron scattering studies.

Contribution

It introduces a method to explicitly compute two-particle spectral functions in a non-integrable spin chain using matrix product states.

Findings

Detailed two-particle spectral functions obtained in the thermodynamic limit.

Identification of subtle features in the spectral function that can be observed experimentally.

Application to a model relevant for spin-Peierls compounds.

Abstract

Interactions between elementary excitations in quasi-one dimensional antiferromagnets are of experimental relevance and their quantitative theoretical treatment has been a theoretical challenge for many years. Using matrix product states, one can explicitly determine the wavefunctions of the one- and two-particle excitations, and, consequently, the contributions to dynamical correlations. We apply this framework to the (non integrable) frustrated dimerized spin-1/2 chain, a model for generic spin-Peierls systems, where low-energy quasi-particle excitations are bound states of topological solitons. The spin structure factor involving two quasi-particle scattering states is obtained in the thermodynamic limit with full momentum and frequency resolution. This allows very subtle features in the two-particle spectral function to be revealed which, we argue, could be seen, e.g., in inelastic neutron scattering of spin-Peierls compounds under a change of the external pressure.