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Quantum effects in rotationally invariant spin glass models.

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This study validates a quasistatic approach for quantum spin glasses, finding it effective for analyzing quantum effects and providing new insights into quantum optimization algorithms.

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Area of Science:

  • Condensed Matter Physics
  • Quantum Mechanics
  • Statistical Mechanics

Background:

  • Investigating quantum effects in transverse-field Ising spin glass models is crucial for understanding complex magnetic phenomena.
  • The conventional static approximation may not fully capture the dynamics of order parameters in quantum spin glasses.

Purpose of the Study:

  • To evaluate the validity of a quasistatic approach for quantum spin glass models.
  • To analyze quantum effects in models with rotationally invariant random interactions.
  • To establish a stability condition for replica symmetric solutions.

Main Methods:

  • Utilized the replica method combined with Suzuki-Trotter decomposition.
  • Established a stability condition analogous to the de Almeida-Thouless criterion.
  • Performed numerical analysis on the Sherrington-Kirkpatrick, Hopfield, and random orthogonal models.

Main Results:

  • Estimated the critical transverse field (Γc) for the Sherrington-Kirkpatrick model, consistent with Monte Carlo results.
  • Provided a novel estimate for Γc in the Hopfield model.
  • Indicated that quantum effects modify the random first-order transition in the random orthogonal model at low temperatures.

Conclusions:

  • The quasistatic treatment is supported for analyzing quantum spin glasses.
  • The findings offer valuable insights for quantum optimization algorithms.
  • Quantum effects significantly influence the behavior of spin glass models.