Bosonic integer quantum Hall effect as topological pumping

TL;DR

This paper models a topological pumping process in a quasi-one-dimensional system that mimics the bosonic integer quantum Hall effect, revealing a novel off-diagonal pumping mechanism linked to polarization changes.

Contribution

It introduces a model of interaction-induced topological pumping based on a quasi-1D limit of quantum Hall states, connecting the BIQH state to the Haldane phase of two-component bosons.

Findings

Identifies the quasi-1D BIQH state as the Haldane phase of two-component bosons.

Demonstrates off-diagonal topological pumping via adiabatic phase transitions.

Interprets pumping mechanism through polarization changes between quantized values.

Abstract

Based on a quasi-one-dimensional limit of quantum Hall states on a thin torus, we construct a model of interaction-induced topological pumping which mimics the Hall response of the bosonic integer quantum Hall (BIQH) state. The quasi-one-dimensional counterpart of the BIQH state is identified as the Haldane phase composed of two-component bosons which form effective spin-$1$ degrees of freedom. An adiabatic change between the Haldane phase and trivial Mott insulators constitute {\it off-diagonal} topological pumping in which the translation of the lattice potential for one component induces a current in the other. The mechanism of this pumping is interpreted in terms of changes in polarizations between symmetry-protected quantized values.