Dynamical signatures of quasiparticle interactions in quantum spin chains

TL;DR

This paper investigates how quasiparticle interactions affect the dynamical susceptibility in quantum spin chains, revealing interaction-induced gaps and bound states through numerical and analytical methods.

Contribution

It provides new insights into the effects of interactions on spinon and magnon excitations in antiferromagnetic chains, including the emergence of gaps and bound states.

Findings

Interaction causes a gap between spinon branches at low magnetization.

Two-magnon bound states appear near saturation magnetization.

Results are supported by matrix-product-state simulations and analytical approximations.

Abstract

We study the transverse dynamical susceptibility of an antiferromagnetic spin$-1/2$ chain in presence of a longitudinal Zeeman field. In the low magnetization regime in the gapless phase, we show that the marginally irrelevant backscattering interaction between the spinons creates a non-zero gap between two branches of excitations at small momentum. We further demonstrate how this gap varies upon introducing a second neighbor antiferromagnetic interaction, vanishing in the limit of a non-interacting "spinon gas". In the high magnetization regime, as the Zeeman field approaches the saturation value, we uncover the appearance of two-magnon bound states in the transverse susceptibility. This bound state feature generalizes the one arising from string states in the Bethe ansatz solution of the integrable case. Our results are based on numerically accurate, unbiased matrix-product-state techniques as well as analytic approximations.