Anomalous fractional quantum Hall effect and multi-valued Hamiltonians

We discuss anomalous fractional quantum Hall effect that exists without external magnetic field. We propose that excitations in such systems may be described effectively by non-interacting particles with the Hamiltonians defined on the Brillouin zone with a branch cut. Hall conductivity of such a system is expressed through the one-particle Green function. We demonstrate that for the Hamiltonians of the proposed type this expression takes fractional values times Klitzing constant. Possible relation of the proposed construction with degeneracy of ground state is discussed as well.

Automated summary

An anomalous fractional quantum Hall effect is discussed, which can exist without an external magnetic field. It is proposed that excitations in such systems may be effectively described by non-interacting particles with Hamiltonians defined on the Brillouin zone with a branch cut. The Hall conductivity of this system is expressed through the one-particle Green function, and for the proposed type of Hamiltonians, this expression takes fractional values times the Klitzing constant. Possible relation of this construction with the degeneracy of the ground state is also discussed.