Dual approach to soft-core anyonic Lieb-Liniger fluids

TL;DR

This paper explores a one-dimensional Bose gas with gauge fields, revealing a mapping to anyonic systems, and uncovers phenomena like roton minima, chiral solitons, and shock waves through analytical and numerical methods.

Contribution

It introduces a dual approach to study soft-core anyonic Lieb-Liniger fluids, combining gauge transformations, mean-field analysis, and numerical simulations to reveal novel quantum and hydrodynamic phenomena.

Findings

Presence of roton minima in the Bogoliubov spectrum

Existence of chiral soliton trains and shock waves

Mapping between Bose gas with gauge fields and anyonic systems

Abstract

The identity of quantum matter can be effectively altered by means of gauge fields. In two spatial dimensions this is illustrated by the Chern-Simons flux-attachment mechanism, but such a mechanism is not possible in lower dimensions. Here, we study a one-dimensional interacting Bose gas in the presence of a gauge field. This model can be explicitly mapped into an interacting anyonic system by a large gauge transformation, indicating a statistical transmutation analogous to that of Chern-Simons. The Bogoliubov spectrum in the weakly-interacting limit reveals the presence of a roton minimum arising from the statistical interaction. At a mean-field level chiral solitons are recovered. Should these be understood as quantum bound states, it is natural to interpret them as corresponding to localised anyonic quasiparticles. Hydrodynamic arguments highlight the presence of dispersive chiral shock waves in the propagation of a wavepacket due to a Riemann-Hopf nonlinearity. Numerical calculations show the presence of both chiral soliton trains and shock waves.