Scattering of spinon excitations by potentials in the 1D Heisenberg model

TL;DR

This paper investigates how spinon excitations in the 1D Heisenberg model scatter off local and phonon potentials using Bethe ansatz and T-matrix methods, revealing size-dependent transmission behaviors linked to critical properties.

Contribution

It provides a semi-analytical analysis of spinon scattering, contrasting with free fermion behavior, and connects scattering phenomena to the dressed charge and topological features of the model.

Findings

Regular scattering coefficients in odd-site chains

Exponential transfer of transmission probability in even-site chains

Link between exponential behavior and dressed charge

Abstract

By a semi-analytical Bethe ansatz method and a T-matrix approach we study the scattering of a spinon, the elementary quantum many-body topological excitation in the 1D Heisenberg model, by local and phonon potentials. In particular, we contrast the scattering of a spinon to that of a free spinless fermion in the XY model to highlight the effect of strong correlations. For the one spinon scattering in an odd-site chain, we find a regular behavior of the scattering coefficients. In contrast, in an even-site chain there is a transfer of transmission probability between the two spinon branches that grows exponentially with system size. We link the exponent of the exponential behavior to the dressed charge that characterizes the critical properties of the 1D Heisenberg model, an interplay of topological and critical properties. The aim of this study is a microscopic understanding of spinon scattering by impurities, barriers or phonons, modeled as prototype potentials, an input in the analysis of quantum spin transport experiments.