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Entanglement growth from squeezing on the MPS manifold.

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Researchers analytically connect Lyapunov spectrum from matrix product state (MPS) projection to entanglement growth. This rigorously establishes the projected Lyapunov spectrum as a new method for characterizing quantum chaos in many-body systems.

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Area of Science:

  • Quantum physics
  • Many-body systems
  • Chaos theory

Background:

  • Characterizing quantum chaos is challenging due to the Schrödinger equation's linearity.
  • Projecting dynamics onto variational manifolds offers a way to recover non-linearity and study classical chaos as a signature of quantum chaos.

Purpose of the Study:

  • To analytically demonstrate the connection between the Lyapunov spectrum from matrix product state (MPS) manifold projection and entanglement growth.
  • To rigorously establish the physical significance of the projected Lyapunov spectrum as a characterization of quantum chaos.

Main Methods:

  • Projection of quantum dynamics onto the matrix product state (MPS) manifold.
  • Analytical demonstration of the link between Lyapunov spectrum and entanglement growth.
  • Analysis of perturbation propagation as bosonic quasi-particles.

Main Results:

  • An analytical connection is established between the Lyapunov spectrum from MPS projection and entanglement growth.
  • Entanglement growth is shown to occur via squeezing a localized distribution on the variational manifold.
  • The number of distinct perturbation channels directly relates to the Lyapunov spectrum.

Conclusions:

  • The projected Lyapunov spectrum is rigorously shown to be physically significant.
  • This spectrum offers a novel method for characterizing quantum chaos in many-body systems.
  • The method provides a link between quantum chaos and classical chaos.