Dynamics of a one-dimensional spinor Bose liquid: a phenomenological approach

TL;DR

This paper presents a phenomenological approach to understanding the dynamics of a one-dimensional spinor Bose liquid, linking magnon dispersion and correlation function singularities to measurable quantities without specific interaction models.

Contribution

It introduces a model-independent method to relate magnon spectrum exponents to measurable derivatives of the dispersion relation and density.

Findings

Magnon dispersion in 1D spinor Bose liquids is periodic with period 2πn.

Correlation functions exhibit power-law singularities at the magnon spectrum.

Exponents of singularities are related to derivatives of the magnon spectrum with respect to momentum and density.

Abstract

The ground state of a spinor Bose liquid is ferromagnetic, while the softest excitation above the ground state is the magnon mode. The dispersion relation of the magnon in a one-dimensional liquid is periodic in the wavenumber q with the period 2\pi n, determined by the density n of the liquid. Dynamic correlation functions, such as e.g. spin-spin correlation function, exhibit power-law singularities at the magnon spectrum, $\omega\to\omega_m(q,n)$. Without using any specific model of the inter-particle interactions, we relate the corresponding exponents to independently measurable quantities $\partial\omega_m/\partial q$ and $\partial\omega_m/\partial n$.