Evolution between quantum Hall and conducting phases: simple models and some results

In this talk, we introduce and study a particularly simple model where kinetic energy, strong correlations, and band topology coexist.

We consider interacting quantum particles in two dimensions in a strong magnetic field such that the Hilbert space is restricted to the Lowest Landau Level (LLL). A periodic potential with a unit cell enclosing one flux quantum broadens the LLL into a dispersive Chern band. This enables an evolution from the familiar quantum Hall regime to large band width limit where a conducting state is expected.

This evolution is studied in detail for the specific case of bosons at filling factor ν=1. In the quantum Hall regime, the ground state at this filling is a gapped quantum hall state (the "bosonic Pfaffian") which may be viewed as descending from a (bosonic) composite Fermi liquid. At large bandwidth, the ground state is a bosonic superfluid.

We show how both phases and their evolution can be described within a single theoretical framework based on a LLL composite fermion construction. Building on our previous work on the bosonic composite Fermi liquid, we show that the evolution into the superfluid can be usefully described by a non-commutative quantum field theory in a periodic potential.