A no-go theorem for the continuum limit of a periodic quantum spin chain

TL;DR

This paper proves that certain quantum spin chains constructed via block spin renormalization cannot have a continuum limit described by a chiral conformal field theory with continuous translation symmetry.

Contribution

It establishes a no-go theorem showing the incompatibility between the lattice construction and the continuum chiral conformal field theory for these models.

Findings

Hilbert space from block spin renormalization does not support chiral CFT

No continuous translation symmetry in the continuum limit

Limits of the lattice model do not yield chiral conformal field theories

Abstract

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.