A no-go theorem for the continuum limit of a periodic quantum spin chain
  We show that the Hilbert space formed from a block spin renormalization construction of a cyclic quantum spin chain (based on the Temperley-Lieb algebra) does not support a chiral conformal field theory whose Hamiltonian generates translation on the circle as a continuous limit of the rotations on the lattice. 
Vaughan F.R. Jones
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