Quantized transport induced by topology transfer between coupled one-dimensional lattice systems

TL;DR

This paper demonstrates that topological pumping in a 1D insulator can induce quantized charge transport in a coupled auxiliary chain, revealing a transfer of topological invariants even in interacting systems.

Contribution

It introduces a method to transfer topological invariants from a 1D insulator to an auxiliary chain, extending topological characterization to interacting systems.

Findings

Quantized charge transport is induced in the auxiliary chain by the topological pump.

The transported charge relates to a topological invariant of the fictitious Hamiltonian.

In interacting systems, this invariant generalizes the TKNN number, capturing topological properties.

Abstract

We show that a topological pump in a one-dimensional (1D) insulator can induce a strictly quantized transport in an auxiliary chain of non-interacting fermions weakly coupled to the first. The transported charge is determined by an integer topological invariant of the ficticious Hamiltonian of the insulator, given by the covariance matrix of single-particle correlations. If the original system consists of non-interacting fermions, this number is identical to the TKNN (Thouless, Kohmoto, Nightinghale, den Nijs) invariant of the original system and thus the coupling induces a transfer of topology to the auxiliary chain. When extended to particles with interactions, for which the TKNN number does not exist, the transported charge in the auxiliary chain defines a topological invariant for the interacting system. In certain cases this invariant agrees with the many-body generalization of the TKNN number introduced by Niu, Thouless, and Wu (NTW). We illustrate the topology transfer to the auxiliary system for the Rice-Mele model of non-interacting fermions at half filling and the extended superlattice Bose-Hubbard model at quarter filling. In the latter case the induced charge pump is fractional.