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Thermal Area Law in Long-Range Interacting Systems.

Donghoon Kim1, Tomotaka Kuwahara1,2,3, Keiji Saito4

  • 1RIKEN Center for Quantum Computing (RQC), Analytical Quantum Complexity RIKEN Hakubi Research Team, Wako, Saitama 351-0198, Japan.

Physical Review Letters
|February 6, 2025
PubMed
Summary
This summary is machine-generated.

The thermal area law in quantum physics holds for interactions decaying as a power law, with a critical exponent αc=(D+1)/2, where D is the spatial dimension. This finding is robust even in unstable regimes and verified numerically.

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Area of Science:

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

Background:

  • The area law for bipartite information is fundamental in quantum many-body physics.
  • It universally holds for mutual information in thermal equilibrium with short-range interactions.
  • Conditions for the thermal area law with power-law decaying interactions (r^{-α}) are not well-understood.

Purpose of the Study:

  • To determine the optimal condition, specifically the critical exponent αc, for the universal validity of the thermal area law.
  • To investigate the robustness of the thermal area law beyond conventional boundary interaction arguments.
  • To establish a precise criterion for the thermal area law in systems with power-law decaying interactions.

Main Methods:

  • Analysis of the boundary interaction magnitude between subsystems.
  • Derivation of the optimal threshold αc = (D+1)/2 based on power-law decay of bipartite correlations.
  • Numerical verification of the derived condition in both integrable and nonintegrable systems.

Main Results:

  • The optimal threshold for the thermal area law is found to be αc = (D+1)/2, where D is the spatial dimension.
  • This condition is remarkably robust, holding even for thermodynamically unstable regimes (α < D).
  • Numerical calculations confirm the qualitative accuracy of this criterion for both integrable and nonintegrable systems.
  • The same criterion α > (D+1)/2 was found to apply to the thermal area law for quantum entanglement, as indicated by logarithmic negativity calculations.

Conclusions:

  • The thermal area law universally holds for power-law decaying interactions when α > (D+1)/2.
  • This criterion is more general than previously thought, encompassing unstable regimes and various system types.
  • An unconditional proof of the thermal area law is possible for α > D above a threshold temperature via the power-law clustering theorem.