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We demonstrate that a driven integrable model, the Lieb-Liniger model with a time-dependent potential, remains integrable. Its quasienergies are calculable via the Bethe ansatz, challenging general expectations for driven systems.

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Area of Science:

  • Quantum mechanics
  • Many-body physics
  • Integrable systems

Background:

  • Periodically driven systems often become nonintegrable, leading to complex dynamics.
  • The Lieb-Liniger model is a fundamental integrable model in quantum many-body physics.

Purpose of the Study:

  • To investigate the integrability of the Lieb-Liniger model under periodic driving with a linear potential.
  • To determine if the system's Floquet Hamiltonian remains integrable and explore its dynamics.

Main Methods:

  • Analysis of the Floquet Hamiltonian for the driven Lieb-Liniger model.
  • Application of the Bethe ansatz approach to calculate quasienergies.
  • Examination of system dynamics at stroboscopic times.

Main Results:

  • The Floquet Hamiltonian of the driven Lieb-Liniger model with a linear potential is shown to be integrable.
  • Quasienergies of the system can be precisely determined using the Bethe ansatz.
  • Insights into the system's behavior at discrete time intervals.

Conclusions:

  • Periodic driving does not necessarily destroy integrability in all quantum models.
  • The Bethe ansatz provides a powerful tool for analyzing driven integrable systems.
  • A potential experimental setup for realizing this driven system is proposed.