Conformal invariance of chiral edge theories

Abstract

The low-energy effective quantum field theory of the edge excitations of a fully-gapped bulk topological phase corresponding to a local interaction Hamiltonian must be local and unitary. Here it is shown that whenever all the edge excitations propagate in the same direction with the same velocity, it is a conformal field theory. In particular, this is the case in the quantum Hall effect for model "special Hamiltonians", for which the ground state, quasihole, and edge excitations can be found exactly as zero-energy eigenstates, provided the spectrum in the interior of the system is fully gapped. In addition, other conserved quantities in the bulk, such as particle number and spin, lead to affine Lie algebra symmetries in the edge theory. Applying the arguments to some trial wavefunctions related to non-unitary conformal field theories, it is argued that the Gaffnian state and an infinite number of others cannot describe a gapped topological phase because the numbers of edge excitations do not match any unitary conformal field theory.

RevTeX, 6 pages. v2: added argument that Gaffnian state cannot be gapped, and additional references. Now 9 pages. v3: minor changes from v2

References in corpus (6)

• Fractional Quantum Hall States and Jack Polynomials
• Generalized Clustering Conditions of Jack Polynomials at Negative Jack Parameter $\alpha$
• Properties of Non-Abelian Fractional Quantum Hall States at Filling $\nu =\frac{k}{r}$
• Pseudopotentials for Multi-particle Interactions in the Quantum Hall Regime
• Filling the Bose sea: symmetric quantum Hall edge states and affine characters
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