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Nearly linear light cones in long-range interacting quantum systems.

Michael Foss-Feig1,2, Zhe-Xuan Gong1,2, Charles W Clark1

  • 1Joint Quantum Institute, NIST/University of Maryland, College Park, Maryland 20742, USA.

Physical Review Letters
|May 2, 2015
PubMed
Summary
This summary is machine-generated.

In quantum systems with long-range interactions, light cone velocity is not exponential. We show that these light cones are polynomially bounded, constraining correlation growth and entanglement in atomic, molecular, and optical systems.

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Area of Science:

  • Quantum physics
  • Condensed matter theory
  • Atomic, molecular, and optical physics

Background:

  • Nonrelativistic quantum theories with short-range interactions exhibit emergent locality defined by a linear light cone.
  • Long-range interacting systems with power-law interactions (1/r^α) present a challenge to this notion of locality.
  • Previous understanding suggested potentially exponential velocity growth in the light cones of such systems.

Purpose of the Study:

  • To investigate the behavior of light cones in quantum systems with power-law interactions.
  • To determine the precise bounds on the spread of influence in these systems.
  • To clarify the constraints on correlation growth and entanglement production.

Main Methods:

  • Analysis of quantum theories with Hamiltonians featuring power-law interactions (1/r^α).
  • Derivation of bounds on the propagation of influences over distance and time.
  • Mathematical analysis of light cone behavior for different values of α relative to system dimension D.

Main Results:

  • Light cones in power-law interacting systems are not unbounded or exponentially growing.
  • For α > 2D, light cone propagation is bounded by a polynomial function of distance.
  • As α approaches infinity, the light cones become linear, similar to short-range systems.

Conclusions:

  • The study rules out exponential velocity growth in the light cones of long-range interacting quantum systems.
  • Results establish polynomial bounds for light cone propagation when α > 2D.
  • These findings impose significant constraints on correlation dynamics and entanglement generation in emerging quantum technologies.