Quantum effects in rotationally invariant spin glass models

• URL: http://arxiv.org/abs/2504.18034v1
• Date: Fri, 25 Apr 2025 03:01:44 GMT
• Title: Quantum effects in rotationally invariant spin glass models
• Authors: Yoshinori Hara, Yoshiyuki Kabashima,
• Abstract summary: This study investigates the quantum effects in transverse-field Ising spin glass models with rotationally invariant random interactions.<n>The primary aim is to evaluate the validity of a quasi-static approximation that captures the imaginary-time dependence of the order parameters.<n>This study supports a quasi-static treatment for analyzing quantum spin glasses and may offer useful insights into the analysis of quantum optimization algorithms.
• Score: 7.834479563217133
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: This study investigates the quantum effects in transverse-field Ising spin glass models with rotationally invariant random interactions. The primary aim is to evaluate the validity of a quasi-static approximation that captures the imaginary-time dependence of the order parameters beyond the conventional static approximation. Using the replica method combined with the Suzuki--Trotter decomposition, we established a stability condition for the replica symmetric solution, which is analogous to the de Almeida--Thouless criterion. Numerical analysis of the Sherrington--Kirkpatrick model estimates a value of the critical transverse field, $\Gamma_\mathrm{c}$, which agrees with previous Monte Carlo-based estimations. For the Hopfield model, it provides an estimate of $\Gamma_\mathrm{c}$, which has not been previously evaluated. For the random orthogonal model, our analysis suggests that quantum effects alter the random first-order transition scenario in the low-temperature limit. This study supports a quasi-static treatment for analyzing quantum spin glasses and may offer useful insights into the analysis of quantum optimization algorithms.

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