Barasat Government College, Barasat, Kolkata 700124, India.
Condensed Matter Physics Division, Saha Institute of Nuclear Physics, 1/AF Bidhannagar, Kolkata 700064, India.
Phys Rev E. 2018 Feb;97(2-1):022146. doi: 10.1103/PhysRevE.97.022146.
We explore the behavior of the order parameter distribution of the quantum Sherrington-Kirkpatrick model in the spin glass phase using Monte Carlo technique for the effective Suzuki-Trotter Hamiltonian at finite temperatures and that at zero temperature obtained using the exact diagonalization method. Our numerical results indicate the existence of a low- but finite-temperature quantum-fluctuation-dominated ergodic region along with the classical fluctuation-dominated high-temperature nonergodic region in the spin glass phase of the model. In the ergodic region, the order parameter distribution gets narrower around the most probable value of the order parameter as the system size increases. In the other region, the Parisi order distribution function has nonvanishing value everywhere in the thermodynamic limit, indicating nonergodicity. We also show that the average annealing time for convergence (to a low-energy level of the model, within a small error range) becomes system size independent for annealing down through the (quantum-fluctuation-dominated) ergodic region. It becomes strongly system size dependent for annealing through the nonergodic region. Possible finite-size scaling-type behavior for the extent of the ergodic region is also addressed.
我们使用蒙特卡罗技术研究了量子 Sherrington-Kirkpatrick 模型在 spin glass 相中的序参量分布行为，该模型的有效 Suzuki-Trotter Hamiltonian 在有限温度和使用精确对角化方法得到的零温度下进行研究。我们的数值结果表明，在模型的 spin glass 相中，除了高温下经典涨落主导的非遍历区域外，还存在一个低温下量子涨落主导的遍历区域。在遍历区域中，随着系统尺寸的增加，序参量分布在最可能的序参量值周围变得更窄。在其他区域中，Parisi 序分布函数在热力学极限下处处具有非零值，表明非遍历性。我们还表明，对于通过（量子涨落主导的）遍历区域的退火，收敛（在小误差范围内达到模型的低能水平）的平均退火时间对于系统尺寸是独立的。而对于通过非遍历区域的退火，它则强烈依赖于系统尺寸。还讨论了遍历区域的扩展的可能有限尺寸标度行为。
