Rotons in Anyon Superfluids*

We compute the spectrum of excitations for anyon superfluids near statistical angle \pi beyond the massless Nambu-Goldstone boson of the superfluid. Modeling the system as fermions at non-zero density coupled to a U(1) Chern-Simons gauge field, we develope an effective theory via the technique of bosonization. The effective theory obtained this way contains an infinite tower of fields and is valid well beyond the cut-off for the effective field theory of the Nambu-Goldstone boson. It captures a much larger part of the spectrum, exhibiting multiple branches of gapped excitations as well as roton minima and maxima.