Fractional Quantum Hall Effect of Lattice Bosons Near Commensurate Flux

TL;DR

This paper investigates the fractional quantum Hall effect in lattice bosons near rational flux, revealing the importance of umklapp and pairing interactions in determining ground states, including stabilization of Moore-Read Pfaffian states.

Contribution

It introduces a multi-species continuum model for lattice bosons near rational flux and highlights the role of non-conserving pseudospin interactions in stabilizing paired quantum Hall states.

Findings

Umklapp processes significantly influence ground state phases.

Paired wavefunctions like Moore-Read Pfaffian are stabilized by these interactions.

Certain wavefunctions are destabilized when umklapp interactions are strong.

Abstract

We study interacting bosons on a lattice in a magnetic field. When the number of flux quanta per plaquette is close to a rational fraction, the low energy physics is mapped to a multi-species continuum model: bosons in the lowest Landau level where each boson is given an internal degree of freedom, or pseudospin. We find that the interaction potential between the bosons involves terms that do not conserve pseudospin, corresponding to umklapp processes, which in some cases can also be seen as BCS-type pairing terms. We argue that in experimentally realistic regimes for bosonic atoms in optical lattices with synthetic magnetic fields, these terms are crucial for determining the nature of allowed ground states. In particular, we show numerically that certain paired wavefunctions related to the Moore-Read Pfaffian state are stabilized by these terms, whereas certain other wavefunctions can be destabilized when umklapp processes become strong.