Characterizing fractional topological phases of lattice bosons near the first Mott lobe

TL;DR

This paper explores various topological phases in the Bose-Hubbard model under magnetic fields near the first Mott lobe, identifying states like Laughlin and Moore-Read through entanglement and conductance analysis.

Contribution

It provides the first detailed characterization of topological bosonic phases near the Mott lobe, including signatures of quantum Hall states and their entanglement spectra.

Findings

Identification of gapped topological phases near the Mott lobe

Signatures of Laughlin, Moore-Read, and Bosonic Integer Quantum Hall states

Entanglement spectra supporting the existence of high-filling topological states

Abstract

The Bose-Hubbard model subjected to an effective magnetic field hosts a plethora of phases with different topological orders when tuning the chemical potential. Using the density matrix renormalization group method, we identify several gapped phases near the first Mott lobe at strong interactions. They are connected by a particle-hole symmetry to a variety of quantum Hall states stabilized at low fillings. We characterize phases of both particle and hole type and identify signatures compatible with Laughlin, Moore-Read, and Bosonic Integer Quantum Hall states by calculating the quantized Hall conductance and by extracting the topological entanglement entropy. Furthermore, we analyze the entanglement spectrum of a Laughlin state of bosonic particles and holes for a range of interaction strengths, as well as the entanglement spectrum of a Moore-Read state. These results further corroborate the existence of topological states at high fillings, close to the first Mott lobe, as hole analogues of the respective low-filling states.