Quantum effects in rotationally invariant spin glass models.

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.