手征随机矩阵系综与扭曲SU（2）格点Dirac谱的普适交叉
Universality crossover between chiral random matrix ensembles and twisted SU(2) lattice Dirac spectra
摘要：
基于类QCD理论Dirac谱在（伪）破实微扰下的统计涨落，在ε区域，我们计算了Dyson-Mehta-Pandey型手征和非手征参量随机矩阵系综的最小本征值分布和能级间距分布.为此，我们采用Nystrom方法来数值计算积分核的Fredholm Pfuman的chG（O，S）E-chGUE和G（O，S）E-GUE交叉。通过与几种格点模型，即SU（2）猝灭格点规范理论在扭曲边界条件（虚化学势）或相位噪声扰动下的基本和伴随交错Dirac谱的比较，我们证实了我们结果的有效性和普适性.在零虚区域和光谱体中，已经在小的4^4晶格上实现了出色的单参数拟合。预期缩放的拟合参数与扭曲的相位，平均能级间距，和系统的大小允许精确确定的π衰变（扩散）常数F在低能量有效拉格朗日。
英文摘要：
Motivated by the statistical fluctuation of Dirac spectrum of QCD-like theories subjected to (pseudo)reality-violating perturbations and in the epsilon-regime, we compute the smallest eigenvalue distribution and the level spacing distribution of chiral and non-chiral parametric random matrix ensembles of Dyson-Mehta-Pandey type. To this end we employ the Nystrom method to numerically evaluate the Fredholm Pfaffian of the integral kernel for the chG(O,S)E-chGUE and G(O,S)E-GUE crossover. We confirm the validity and universality of our results by comparing them with several lattice models, namely fundamental and adjoint staggered Dirac spectra of SU(2) quenched lattice gauge theory under the twisted boundary condition (imaginary chemical potential) or perturbed by phase noise. Both in the zero-virtuality region and in the spectral bulk, excellent one-parameter fitting is achieved already on a small 4^4 lattice. Anticipated scaling of the fitting parameter with the twisting phase, mean level spacing, and the system size allows for precise determination of the pion decay (diffusion) constant F in the low-energy effective Lagrangian.
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