A Magnetic Model with a Possible Chern-Simons Phase

  title={A Magnetic Model with a Possible Chern-Simons Phase
  author={Michael H. Freedman},
  journal={Communications in Mathematical Physics},
  • M. Freedman
  • Published 9 October 2001
  • Physics, Mathematics
  • Communications in Mathematical Physics
Abstract: An elementary family of local Hamiltonians , is described for a 2-dimensional quantum mechanical system of spin particles. On the torus, the ground state space Gŝ,ℓ is (log) extensively degenerate but should collapse under ``perturbation'' to an anyonic system with a complete mathematical description: the quantum double of the SO(3)-Chern-Simons modular functor at q=e2πi/ℓ+2 which we call DEℓ. The Hamiltonian Hŝ,ℓ defines a quantum loop gas. We argue that for ℓ=1 and 2, G○,ℓ is… Expand
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