Driven Topological Systems in the Classical Limit

TL;DR

This paper explores the classical analog of driven topological quantum systems, demonstrating how classical interactions influence edge currents and can provide insights into quantum behaviors.

Contribution

It introduces a classical counterpart to a quantum driven topological model, analyzing the effects of interactions and comparing classical and quantum edge currents.

Findings

Interactions act as time-dependent disorder in the classical system.

Mean-field theory accurately describes the classical dynamics.

Classical insights can inform understanding of quantum edge currents.

Abstract

Periodically-driven quantum systems can exhibit topologically non-trivial behaviour, even when their quasi-energy bands have zero Chern numbers. Much work has been conducted on non-interacting quantum-mechanical models where this kind of behaviour is present. However, the inclusion of interactions in out-of-equilibrium quantum systems can prove to be quite challenging. On the other hand, the classical counterpart of hard-core interactions can be simulated efficiently via constrained random walks. The non-interacting model proposed by Rudner et al. [Phys. Rev. X 3, 031005 (2013)], has a special point for which the system is equivalent to a classical random walk. We consider the classical counterpart of this model, which is exact at a special point even when hard-core interactions are present, and show how these quantitatively affect the edge currents in a strip geometry. We find that the interacting classical system is well described by a mean-field theory. Using this we simulate the dynamics of the classical system, which show that the interactions play the role of Markovian, or time dependent disorder. By comparing the evolution of classical and quantum edge currents in small lattices, we find regimes where the classical limit considered gives good insight into the quantum problem.