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We reexamined snapshot entropy in Ising and Potts models. The findings suggest a connection between snapshot entropy and holographic entanglement entropy, particularly after proper spin snapshot encoding.

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Area of Science:

  • Statistical Mechanics
  • Quantum Information Theory
  • Condensed Matter Physics

Background:

  • Snapshot entropy offers a novel approach to analyzing critical phenomena in statistical models.
  • Understanding the relationship between classical spin systems and quantum entanglement is a key challenge.

Purpose of the Study:

  • To investigate the scaling behavior of snapshot entropy in the Ising and three-states Potts models.
  • To explore the connection between snapshot entropy and holographic entanglement entropy.
  • To analyze the impact of spin snapshot encoding on entropy scaling.

Main Methods:

  • Analysis of the Ising and three-states Potts models on an L×L square lattice.
  • Examination of snapshot entropy with different encoding strategies (proper and coarse-grained).
  • Asymptotic scaling analysis of entropy at the critical temperature (T(c)).

Main Results:

  • At T(c), snapshot entropy scales as S∼(1/3)lnL, similar to 1D quantum critical systems.
  • Proper encoding reveals a connection between snapshot entropy and holographic entanglement entropy.
  • Coarse-grained snapshot entropy exhibits anomalous scaling S(χ)∼χ(η)lnχ even with proper encoding.

Conclusions:

  • Snapshot entropy, particularly after proper encoding, provides insights into holographic entanglement entropy.
  • The behavior of snapshot entropy is influenced by the regulation of the largest singular value of the snapshot matrix.
  • This study bridges concepts from statistical mechanics and quantum information theory through spin snapshot analysis.