A no-go theorem for the continuum limit of a periodic quantum spin chain. (English) Zbl 1397.82025

It is established (see Section 4) 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 a translation on the circle as a continuous limit of the rotations on the lattice.


82B28 Renormalization group methods in equilibrium statistical mechanics
81T40 Two-dimensional field theories, conformal field theories, etc. in quantum mechanics
17B81 Applications of Lie (super)algebras to physics, etc.
22E70 Applications of Lie groups to the sciences; explicit representations
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