论文标题
量子随机能模型的光谱分析
Spectral Analysis of the Quantum Random Energy Model
论文作者
论文摘要
量子随机模型（QREM）是安德森类型的随机矩阵，它描述了横向磁场对德里达自旋玻璃的影响。该模型表现出玻璃相以及经典和量子顺磁性相。我们详细分析了低能频谱，并为QREM的相应特征向量建立了定位 - 偏置转变。基于随机矩阵和运算符技术的组合以及随机几何形状的见解，我们在参数空间的所有范围内得出了基于基态能量和特征向量的近代领导顺序渐近。基于此，我们还推断出自由能的临时领先顺序，事实证明这是确定性的，并且在QREM的所有阶段中的系统大小中的一个顺序。结果，我们确定自旋玻璃制度中自由能的波动的性质。
The Quantum Random Energy Model (QREM) is a random matrix of Anderson-type which describes effects of a transversal magnetic field on Derrida's spin glass. The model exhibits a glass phase as well as a classical and a quantum paramagnetic phase. We analyze in detail the low-energy spectrum and establish a localization-delocalization transition for the corresponding eigenvectors of the QREM. Based on a combination of random matrix and operator techniques as well as insights in the random geometry, we derive next-to-leading order asymptotics for the ground-state energy and eigenvectors in all regimes of the parameter space. Based on this, we also deduce the next-to-leading order of the free energy, which turns out to be deterministic and on order one in the system size in all phases of the QREM. As a result, we determine the nature of the fluctuations of the free energy in the spin glass regime.
