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Dynamical Quantum Phase Transitions: A Geometric Picture.

Johannes Lang1, Bernhard Frank1, Jad C Halimeh1,2

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Summary
This summary is machine-generated.

A simple semiclassical approximation accurately predicts the Loschmidt echo in large quantum many-body systems, offering a new framework for understanding dynamics.

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Area of Science:

  • Quantum Many-Body Physics
  • Statistical Mechanics
  • Quantum Information

Background:

  • The Loschmidt echo quantifies quantum system sensitivity to perturbations.
  • Precise calculation for large systems is computationally demanding.
  • Approximations for quantum dynamics are often considered unreliable.

Purpose of the Study:

  • To investigate the applicability of semiclassical approximations to the Loschmidt echo.
  • To develop a computationally tractable method for analyzing quantum many-body dynamics.
  • To establish a unified framework connecting Loschmidt echo and order parameter dynamics.

Main Methods:

  • Utilized the fully connected transverse-field Ising model as a test case.
  • Employed a simple semiclassical approximation for time evolution.
  • Compared semiclassical results with exact quantum-mechanical calculations.

Main Results:

  • Semiclassical approximation shows good quantitative agreement with exact calculations.
  • The method successfully captures the dynamical phase diagram.
  • An intuitive geometric interpretation of fidelity return rate was developed.

Conclusions:

  • Semiclassical methods are viable for studying Loschmidt echo in mean-field systems.
  • The new framework links order parameter dynamics and Loschmidt echo.
  • This approach offers insights into quantum system behavior at various temperatures.