We study the quantum field theory of non-relativistic bosons coupled to a Chern-Simons gauge field at nonzero particle density. This field theory is relevant to the study of anyon superconductors in which the anyons are described as bosons with a statistical interaction. We show that it is possible to find a mean field solution to the equations of motion for this system which has some of the features of Bose condensation. The mean field solution consists of a lattice of vortices each carrying a single quantum of statistical magnetic flux. We speculate on the effects of the quantum corrections to this mean field solution. We argue that the mean field solution is only stable under quantum corrections if the Chern-Simons coefficient N=2πθ/g2 is an integer. Consequences for anyon superconductivity are presented. A simple explanation for the Meissner effect in this system is discussed.
Mean-Field Solution of the Weak-Strong Cluster Problem for Quantum Annealing with Stoquastic and Non-Stoquastic Catalysts
