On the gauge theory of antiferromagnetism in two dimensions: neutral fermions, quantum Hall effect and physical realization of the parity anomaly

Abstract

An attempt to classify antiferromagnetic ground states in two spatial dimensions according with discrete symmetries is undertaken. The parity violated antiferromagnetic ground states are proposed. Their excitations obey a paraspin and parastatistics and are described by a nonlinear σ-model with the Chern–Simons term. It is conjectured that strongly correlated electrons form a Wigner crystal or incompressible liquid at some preferred band filling factors. The antiferromagnetic ground state with abnormal parity is interpreted as a Mott insulator with fractional filling. The analogue with the quantum Hall effect is discussed. The model introduced reduces the problem of the derivation of the Chern–Simons term to the Hall effect on a lattice and gives a physical realization of the parity anomaly.