Mechanism of particle-flux separation and generation of the dynamical gauge field in the Chern-Simons theory with fermions

Abstract

We study the nonperturbative aspects of the Chern-Simons (CS) gauge theory coupled with fermions by using spatial-lattice regularization. This system is relevant to (i) the composite-fermion approach to the fractional quantum Hall effect, and (ii) the fermionic description of the s = 1 2 quantum XY spin model. It is expected that there are (at least) two phases in this system: One is the constrained phase in which the CS constraint is respected by quasiparticles, so certain amount of gauge fluxes are to be attached to each fermion. The other is the dynamical phase in which the CS constraint is irrelevant to the quasiparticles, and a dynamical gauge field is generated as an independent field. We call this phenomenon of irrelevance of the CS constraint to the quasiparticles a particle-flux separation (PFS), since particles and fluxes do not constrain each other. This PFS is characterized through the dynamics of an auxiliary gauge field that glues particles and CS fluxes, and bears very close resemblance to the phenomenon of charge-spin separation in the strongly correlated electron system for high- T c, superconductivity. We show that there is a confinement-deconfinement (CD) phase transition in the gauge dynamics in question, which is of the same type as the Kosterlitz-Thouless (KT) transition of the classical XY model in two dimensions. The critical temperature T CD is calculable and dependent the CS coefficient and the density of fermions. The constrained phase is identified with the confinement phase of gauge dynamics at T > T CD, while the dynamical phase with PFS is identified with the deconfinement phase at T < T CD. This result is applicable to the system of electrons in a uniform magnetic field at Landau filling factor v = 1 2 . That is, there appears a dynamical gauge field that interacts weakly with the so-called composite fermions. This justifies several existing analyses based on perturbation theory, which conclude non-Fermi-liquid-like behavior of the fermionic quasiparticles.