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

We show that a topological pump in a one-dimensional insulator can induce a strictly quantized transport in an auxiliary chain of noninteracting fermions weakly coupled to the first. The transported charge is determined by an integer topological invariant of the fictitious Hamiltonian of the insulator, given by the covariance matrix of single-particle correlations. If the original system consists of noninteracting fermions, this number is identical to the Thouless, Kohmoto, Nightingale, and den Nijs (TKNN) 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. We illustrate the topology transfer to the auxiliary system for the Rice-Mele model of noninteracting fermions at half filling and the extended superlattice Bose-Hubbard model at quarter filling. In the latter case the induced charge pump is fractional.

Automated summary

The study demonstrates that a topological pump in a one-dimensional insulator can cause strictly quantized transport in an auxiliary chain of noninteracting fermions, with the transported charge determined by an integer topological invariant of the insulator's fictitious Hamiltonian. This number is identical to the TKNN invariant of the original system in the case of noninteracting fermions, while in interacting systems, the transported charge defines a topological invariant. In certain cases, this invariant agrees with the many-body generalization of the TKNN number.