Roton-phonon excitations in Chern-Simons matter theory at finite density

TL;DR

This paper studies the excitations in a Chern-Simons scalar theory at finite density, revealing a superfluid ground state with roton-phonon spectrum similar to quantum Hall systems.

Contribution

It identifies a novel Bose condensed ground state in SU(N) Chern-Simons theory and computes its fluctuation spectrum, including roton and phonon modes.

Findings

Existence of a massless phonon with linear dispersion.

Presence of a roton minimum in the excitation spectrum.

Universal dispersion relations in the massless scalar case.

Abstract

We consider SU(N) Chern-Simons theory coupled to a scalar field in the fundamental representation at strictly zero temperature and finite chemical potential for the global U(1)_B particle number or flavour symmetry. In the semiclassical regime we identify a Bose condensed ground state with a vacuum expectation value (VEV) for the scalar accompanied by noncommuting background gauge field matrix VEVs. These matrices coincide with the droplet ground state of the Abelian quantum Hall matrix model. The ground state spontaneously breaks U(1)_B and Higgses the gauge group whilst preserving spatial rotations and a colour-flavour locked global U(1) symmetry. We compute the perturbative spectrum of semiclassical fluctuations for the SU(2) theory and show the existence of a single massless state with a linear phonon dispersion relation and a roton minimum (and maximum) determining the Landau critical superfluid velocity. For the massless scalar theory with vanishing self interactions, the semiclassical dispersion relations and location of roton extrema take on universal forms.