A self-sustained topological pump

The Thouless pump is a paradigmatic example for a dynamical topological process in non-interacting 1+1-dimensional lattice systems [1]. Cyclic variation of lattice parameters can lead to quantized transport of particles protected by a topological invariant. Until now theoretical as well as experimental approaches for these pumps rely on direct modulation of the lattice parameters in time. Recent experiments [2] have shown, that replacing the lattice parameter by dynamical quantum degrees of freedom can lead to self-sustained topological pumps. We here present a theoretical model, where a single spin controlling the lattice particles and being subject to a constant magnetic field ”drives” the system into a pumping phase without explicit time-dependencies. This pumping phase represents a non-equilibrium topological phase in excited eigenstates of the interacting system. We numerically determine the phase diagram of the system with parameter regions of quantized topological transport in the excited eigenstate and trivial phases without quantized transport. We derive analytic approximations for the corresponding critical parameters and introduce a topological invariant governing the topological transport.

[1] D. J. Thouless, Phys. Rev. B 27, 6083 (1983)

[2] D. Dreon, et al., Nature 608, 494-498 (2022)