Strongly coupled massive QCD3 and frustrated Heisenberg antiferromagnets: fractional statistics and chiral-spin order |
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| Affiliation: | 1. National Institute for Theoretical Physics, School of Physics and Centre for Theoretical Physics, University of the Witwatersrand, Wits 2050, South Africa;2. Centre for Research in String Theory, School of Physics and Astronomy, Queen Mary University of London, Mile End Road, London E1 4NS, UK;1. Department of Theoretical Physics, Tomsk State Pedagogical University, 634061, Tomsk, Russia;2. National Research Tomsk State University, 634050, Tomsk, Russia;3. Bogoliubov Laboratory of Theoretical Physics, JINR, 141980 Dubna, Moscow region, Russia;4. Tomsk State University of Control Systems and Radioelectronics, 634050 Tomsk, Russia;1. Yerevan State University, 1 Alex Manoogian Street, Yerevan 0025, Armenia;2. Tomsk Polytechnic University, Lenin Avenue 30, 634050 Tomsk, Russia |
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| Abstract: | 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. |
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