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

TL;DR

This paper investigates the transition from quantum Hall states to conducting phases in simple models of interacting bosons under strong magnetic fields, revealing a continuous evolution from topological insulators to superfluids.

Contribution

It introduces a unified theoretical framework using composite fermion construction and non-commutative quantum field theory to describe phase evolution in quantum Hall systems.

Findings

Quantum Hall state at ν=1 is a bosonic Pfaffian with a gap.

Large bandwidth leads to a bosonic superfluid.

Evolution between phases can be modeled within a single theoretical framework.

Abstract

Quantum many particle systems in which the kinetic energy, strong correlations, and band topology are all important pose an interesting and topical challenge. Here we introduce and study particularly simple models where all of these elements are present. 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). This is the familiar quantum Hall regime with rich physics determined by the particle filling and statistics. A periodic potential with a unit cell enclosing one flux quantum broadens the LLL into a Chern band with a finite bandwidth. The states obtained in the quantum Hall regime evolve into conducting states in the limit of large bandwidth. We study this evolution in detail for the specific case of bosons at filling factor $\nu = 1$. 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.