Autonomous Thouless Pump and non-equilibrium topological phases

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 encircling a critical point in parameter space lead to quantized transport of particles in that lattice protected by a topological invariant. By 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, however, that replacing the lattice parameter by dynamical degrees of freedom subject to cw drive and losses can lead to self-sustained, i.e. autonomous topological pumps.

We here present various theoretical models, were the interplay between cw external drive, dissipation and interactions drives the system into a limit-cycle pumping phase without explicit time-dependencies. Specifically we consider a fermionic Rice-Mele chain coupled to either one or many rotating spins which control on-site energies and hopping amplitudes. We investigate both the quantum (small spins) and the mean-field limit (large spins) and the transition between the two. The many-body polarization introduced by Resta [3] shows a non-vanishing winding which identifies a non-trivial, non-equilibrium topological phase. The limit-cycle character of the steady state of the system guarantees a robust, autonomous operation of the topological pump.

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

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

[3] R. Resta, Phys. Rev. Lett. 80, 1800 (1998)