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Time-Dependent Neural Galerkin Method for Quantum Dynamics.

Alessandro Sinibaldi1,2, Douglas Hendry1,2, Filippo Vicentini3,4

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This summary is machine-generated.

We developed a new computational method for quantum dynamics using a global variational principle. This approach efficiently simulates long-time quantum system evolution, revealing ergodicity breaking in 2D models.

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Area of Science:

  • Computational Physics
  • Quantum Dynamics
  • Quantum Many-Body Systems

Background:

  • Simulating quantum dynamics is computationally challenging, especially for long timescales.
  • Traditional time-stepping methods struggle with accuracy and efficiency for complex quantum systems.
  • Variational methods offer a promising avenue but often face limitations in capturing long-time behavior.

Purpose of the Study:

  • Introduce a novel classical computational method for quantum dynamics.
  • Develop a scheme that efficiently simulates the entire quantum state trajectory over a finite time window.
  • Enable the study of previously inaccessible dynamical regimes in strongly interacting quantum systems.

Main Methods:

  • Employ a global-in-time variational principle to enforce Schrödinger's equation.
  • Utilize a Galerkin-inspired Ansatz with time-dependent neural quantum states for variational state parametrization.
  • Minimize a global loss function to compute the quantum state trajectory.

Main Results:

  • Successfully simulated global quantum quenches in 1D and 2D transverse-field Ising models.
  • Uncovered signatures of ergodicity breaking in 2D systems.
  • Observed the absence of thermalization in two-dimensional simulations.

Conclusions:

  • The proposed method is competitive with state-of-the-art time-dependent variational approaches.
  • The global variational principle effectively bounds errors and is well-suited for long-time dynamics.
  • This approach unlocks new possibilities for simulating complex quantum phenomena.