Rotons in anyon superfluids

Abstract

We consider the problem of calculating the excitation spectrum of a gas of nonrelativistic anyons. When the anyons have statistics close to fermionic and the statistical angle has the form θ = π(1 − frac{1}{k} ) where k is a large integer, the problem can be solved by employing the method of bosonization, which maps the problem to that of an infinite number of bosonic excitations coupled to a U(1) Chern-Simons gauge field. The spectrum consists of a Goldstone boson branch and a large number of massive branches, each having roton minima and maxima. The dispersion curves asymptote to the Landau levels at large momentum.