论文标题
粒子孔对称系统中光谱波动的普遍过渡
Universal transition of spectral fluctuation in particle-hole symmetric system
论文作者
论文摘要
我们研究了在随机矩阵设置中具有颗粒 - 孔对称性的多参数系统的光谱特性。我们观察到从泊松到wigner-dyson的交叉行为，就像单个矩阵频谱内间距的平均局部比例一样，是有效的单参数的函数，称为复杂性参数。间距的平均局部比率在整个过渡过程中的复杂性参数方面有所不同。对于受到相同矩阵约束（例如粒子 - 孔对称性）的不同合奏，这种行为是通用的。通过研究用粒子孔对称性与手性对称性的插值集合连接系统，进一步确定了这种依赖性的普遍性。对于每个插值集合，行为在复杂性参数中保持对数。如果2D Su-Schrieffer-Heeger（SSH）（如模型）以及对数依赖性对复杂性参数的依赖性，我们验证了光谱波动的这种普遍性，以验证从集成限制到不可构成极限期间间距的比率。
We study the spectral properties of a multiparametric system having particle-hole symmetry in random matrix setting. We observe a crossover from Poisson to Wigner-Dyson like behavior in average local ratio of spacing within a spectrum of single matrix as a function of effective single parameter referred to as complexity parameter. The average local ratio of spacing varies logarithmically in complexity parameter across the transition. This behavior is universal for different ensembles subjected to same matrix constraint like particle-hole symmetry. The universality of this dependence is further established by studying interpolating ensemble connecting systems with particle-hole symmetry to that with chiral symmetry. For each interpolating ensemble the behavior remains logarithmic in complexity parameter. We verify this universality of spectral fluctuation in case of a 2D Su-Schrieffer-Heeger (SSH) like model along with the logarithmic dependence on complexity parameter for ratio of spacing during transition from integrable to non-integrable limit.
