Bosonic Analogs of Fractional Quantum Hall State in the Vicinity of Mott States

TL;DR

This paper explores bosonic analogs of fractional quantum Hall states near Mott insulators in the Bose-Hubbard model, identifying conditions for their formation and comparing their energies to other phases.

Contribution

It introduces a theoretical framework combining Gutzwiller approximation and Chern-Simons gauge theory to analyze bosonic FQH states in lattice systems.

Findings

Bosonic FQH states have lower energy than Bose-metal phases.

Vortex solid forms at small NN repulsions, transitioning to Bose-metal with increased repulsion.

Conditions for composite fermion emergence are clarified using lattice CS theory.

Abstract

In the present paper, the Bose-Hubbard model (BHM) with the nearest-neighbor (NN) repulsions is studied from the view point of possible bosonic analogs of the fractional quantum Hall (FQH) state in the vicinity of the Mott insulator (MI). First, by means of the Gutzwiller approximation, we obtain the phase diagram of the BHM in a magnetic field. Then, we introduce an effective Hamiltonian describing excess particles on a MI and calculate the vortex density, momentum distribution and the energy gap. These calculations indicate that the vortex solid forms for small NN repulsions, but a homogeneous featureless `Bose-metal' takes the place of it as the NN repulsion increases. We consider particular filling factors at which the bosonic FQH state is expected to form. Chern-Simons (CS) gauge theory to the excess particle is introduced, and a modified Gutzwiller wave function, which describes bosons with attached flux quanta, is introduced. The energy of the excess particles in the bosonic FQH state is calculated using that wave function, and it is compared with the energy of the vortex solid and Bose-metal. We found that the energy of the bosonic FQH state is lower than that of the Bose-metal and comparable with the vortex solid. Finally, we clarify the condition that the composite fermion appears by using CS theory on the lattice that we previously proposed for studying the electron FQH effect.