Dynamical Quantum Phase Transitions: A Geometric Picture

Johannes Lang, Bernhard Frank, and Jad C. Halimeh
Phys. Rev. Lett. 121, 130603 – Published 25 September 2018
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Abstract

The Loschmidt echo is a purely quantum-mechanical quantity whose determination for large quantum many-body systems requires an exceptionally precise knowledge of all eigenstates and eigenenergies. One might therefore be tempted to dismiss the applicability of any approximations to the underlying time evolution as hopeless. However, using the fully connected transverse-field Ising model as an example, we show that this indeed is not the case and that a simple semiclassical approximation to systems well described by mean-field theory is, in fact, in good quantitative agreement with the exact quantum-mechanical calculation. Beyond the potential to capture the entire dynamical phase diagram of these models, the method presented here also allows for an intuitive geometric interpretation of the fidelity return rate at any temperature, thereby connecting the order parameter dynamics and the Loschmidt echo in a common framework. Videos of the postquench dynamics provided in Supplemental Material visualize this new point of view.

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  • Received 15 May 2018
  • Revised 1 August 2018

DOI:https://doi.org/10.1103/PhysRevLett.121.130603

© 2018 American Physical Society

Physics Subject Headings (PhySH)

Statistical Physics & ThermodynamicsCondensed Matter, Materials & Applied Physics

Authors & Affiliations

Johannes Lang1, Bernhard Frank1, and Jad C. Halimeh2,1

  • 1Physik Department, Technische Universität München, 85747 Garching, Germany
  • 2Max Planck Institute for the Physics of Complex Systems, 01187 Dresden, Germany

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Issue

Vol. 121, Iss. 13 — 28 September 2018

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