Strongly coupled massive QCD3 and frustrated Heisenberg antiferromagnets: fractional statistics and chiral-spin order Original Research Article

Strongly coupled massive SU(NC) and U(NC) QCD3 on a lattice is studied using the 1/NC expansion. The quark mass terms have a definite sign in the present model, and therefore the system explicitly breaks the parity symmetry. The continuum counterpart generates the Maxwell + Chern-Simons theory by integrating out the quark field. In the present paper, we shall integrate out the gauge fields using the strong-coupling expansion and obtain a frustrated quantum Heisenberg model as an effective model. The ground state of the above effective quantum spin model is studied using the large-NC approximation. There are two phases; one is a Neel-ordered state and the other is a state with a chiral-spin order. It is explicitly shown that the chiral-spin ordered state corresponds to a state with spontaneous generation of color magnetic flux in the original theory and fractional statistics appears in that phase. This result strongly suggests that there are (at least) two phases in the massive QCD3 and Maxwell-CS theory. One is the confinement phase and the other is the perturbative deconfinement phase with fractional-statistics excitations.