Hydrodynamics of interacting spinons in the magnetized spin-$1/2$ chain with the uniform Dzyaloshinskii-Moriya interaction

TL;DR

This paper uses a hydrodynamic approach to analyze the dynamic spin susceptibility in a spin-$1/2$ Heisenberg chain with Dzyaloshinskii-Moriya interaction, revealing multiple excitation modes and their experimental implications.

Contribution

It provides a novel hydrodynamic analysis of spinon interactions in the presence of Dzyaloshinskii-Moriya interaction and external magnetic fields, with analytical and numerical results.

Findings

Multiple spin excitation modes depending on magnetic field orientation.

Finite energy splitting between optical branches due to backscattering.

Avoided crossing of spin branches at finite momentum influenced by magnetic fields.

Abstract

We use a hydrodynamic approach to investigate dynamic spin susceptibility of the antiferromagnetic spin-$1/2$ Heisenberg chain with a uniform Dzyaloshinskii-Moriya (DM) interaction in the presence of an external magnetic field. We find that transverse (with respect to the magnetic field) spin susceptibility harbors two (respectively, three) spin excitation modes when the magnetic field is parallel (respectively, orthogonal) to the DM axis. In all cases, the marginally irrelevant backscattering interaction between the spinons creates a finite energy splitting between optical branches of excitations at $k = 0$. Additionally, for the orthogonal geometry, the two lower spin branches exhibit avoided crossing at finite momentum which is determined by the total magnetic field (the sum of the external and internal molecular fields) acting on spinons. Our approximate analytical calculations compare well with numerical results obtained using matrix-product-state (MPS) techniques. Physical consequences of our findings for the electron spin resonance experiments are discussed in detail.