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Geometric quantum drives and topological dynamical responses: Hyperbolically driven quantum systems and beyond

Jihong Wu1, Chuan Liu1, Daniel Bulmash2, and Wen Wei Ho1,3,*

  • *Contact author: wenweiho@nus.edu.sg
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Phys. Rev. B 114, 185109 – Published 8 September, 2026

DOI: https://doi.org/10.1103/3m9h-n9w3

Abstract

We introduce a geometrical framework to construct a large class of time-dependent quantum systems in which the position of a classical particle moving autonomously on a smooth connected manifold is used to steer a quantum Hamiltonian over time. This results in quantum drives with structured temporal profiles and properties dependent on the local and global nature of the underlying choice of manifold. We show that our construction recovers the well-known classes of periodically driven and quasiperiodically driven quantum systems, but also unveils fundamentally new classes of quantum dynamics: by utilizing a compact two-dimensional hyperbolic Bolza surface and a nonorientable Klein-bottle surface, we demonstrate examples of a hyperbolically driven quantum system and a nonorientably driven quantum system respectively. Furthermore, we demonstrate that these driven systems exhibit unusual quantized dynamical responses reflecting their different underlying topologies, under the condition of being fully gapped and in the adiabatic limit, and which have interpretations as quantized crystalline electromagnetic responses in certain exotic effective tight-binding lattice models. We envision geometric quantum driving as a general framework to chart the landscape of time-dependent quantum systems and investigate the universal phase structures they exhibit, as well as a useful tool to enhance the capabilities of modern day quantum simulators.

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Phys. Rev. B 114, 185109– Published 8 September, 2026
  • Received 19 March 2025
  • Revised 30 March 2026
  • Accepted 19 August 2026
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