Dynamics of Quantum Chiral Solitons

TL;DR

This paper develops a non-perturbative lattice framework for quantizing chiral solitons in quantum spin chains, revealing their unique dynamics and experimental signatures, especially distinguishing half-odd-integer from integer spins.

Contribution

It introduces a lattice extension of the sine-Gordon/Thirring duality, explicitly constructs quantum chiral-soliton operators, and links their dynamics to observable neutron scattering signatures.

Findings

Soliton tunneling amplitude sign alternates with spin type.

Chiral excitations significantly influence the dynamical spin structure factor.

The framework bridges continuum dualities with lattice models in quantum spin chains.

Abstract

We introduce a non-perturbative framework for quantizing chiral solitons in interacting quantum spin chains. This approach provides a direct lattice extension of the well-established $S$-duality between the sine-Gordon and Thirring models, thereby bridging the gap between continuum dualities and their lattice counterparts. By constructing the quantum chiral-soliton operators explicitly, we show how their unconventional dynamics appear in the excitation spectrum and correlation functions across the full Brillouin zone. A key result is that the dominant soliton tunneling amplitude alternates in sign, $\operatorname{sgn}(t_{1+}) = (-1)^{2S+1}$, sharply distinguishing half-odd-integer from integer spin chains. We further identify characteristic signatures of these chiral excitations in the dynamical spin structure factor, demonstrating their visibility in inelastic neutron scattering. Our results open a route to experimentally probing non-perturbative features of dual quantum field theories in condensed-matter settings.