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Entanglement entropy changes are limited by boundary area in long-range interacting quantum systems (α>D+1). Ground states obey the entanglement area law under specific conditions (α>2D+2), generalizing short-range findings.

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Area of Science:

  • Quantum Information Theory
  • Condensed Matter Physics
  • Statistical Mechanics

Background:

  • Long-range interacting systems exhibit unique quantum phenomena.
  • Entanglement entropy quantifies quantum correlations and is crucial for understanding quantum states.
  • The entanglement area law, typically observed in short-range systems, is a key concept in quantum many-body physics.

Purpose of the Study:

  • To investigate the dynamics of entanglement entropy in D-dimensional lattice spin systems with long-range interactions.
  • To establish bounds on the rate of change of entanglement entropy for these systems.
  • To determine conditions under which the entanglement area law holds for ground states of long-range interacting Hamiltonians.

Main Methods:

  • Derivation of bounds on entanglement entropy evolution rates for arbitrary states.
  • Analysis of ground state properties using adiabatic transformations.
  • Mathematical proofs based on the properties of 1/r^{α} long-range interactions.

Main Results:

  • Entanglement entropy change is bounded by the boundary area for interactions with α>D+1.
  • The entanglement area law is satisfied by ground states for α>2D+2, provided they are adiabatically connected to known area-law satisfying states.
  • These findings extend previous results from short-range interacting systems.

Conclusions:

  • The study provides fundamental insights into the behavior of entanglement in complex quantum systems.
  • The derived bounds are essential for understanding dynamical and quantum phase transitions in systems with long-range interactions.
  • The results pave the way for exploring quantum information processing and condensed matter phenomena in novel settings.