标题： 旋转不变自旋玻璃模型中的量子效应 显示英文标题

标题： Quantum effects in rotationally invariant spin glass models

摘要： 本研究调查了具有旋转不变随机相互作用的横场伊辛自旋玻璃模型中的量子效应。主要目标是评估准静态近似的有效性，该近似捕获了序参量在传统静态近似之外的虚时间依赖性。利用复制方法结合 Suzuki-Trotter 分解，我们建立了复制对称解的稳定性条件，这类似于 de Almeida-Thouless 准则。Sherrington-Kirkpatrick 模型的数值分析估计了临界横场的值 $\Gamma_\mathrm{c}$，该值与先前基于蒙特卡洛的估算一致。对于 Hopfield 模型，它提供了 $\Gamma_\mathrm{c}$的估算值，这一值之前未被评估。对于随机正交模型，我们的分析表明量子效应在低温极限下改变了随机一级相变情景。本研究支持用于分析量子自旋玻璃的准静态处理，并可能为量子优化算法的分析提供有用的见解。 显示英文摘要

摘要： 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.