一维准无序系统中的临界相研究

Studies on the critical phases of one-dimensional quasi-disordered systems

为了研究一维准无序系统中临界相的性质,运用精确对角化的数值方法计算一维Aubry-André模型和非对角Aubry-André模型中临界相的能级差比率.结果表明:对一维单体系统,可以用能级差比率的方法区分不同的相,在不加随机相位的情况下能够直接确定扩展相、临界相、局域相的范围;加入随机相位后,扩展相能级差比率的统计平均值并不呈现多体系统中的高斯正交分布;同一个模型中,临界相能级差比率的统计平均值恒定.

It was studied the properties of the critical phase in one dimensional quasi-disordered system,the difference ratio of the critical phase in the one-dimensional Aubry-André model and off-diagonal Aubry-Andréis calculated by using the exact diagonalization method. The results showed that the ratio of adjacent gap could be used to distinguish the different phases in one-dimensional systems,and could be directly used to determine the different phases without adding random offsets. After adding the random offset,the average value of the ratio of the adjacent gap in the extended states was different from the result in many-body system,and did not satisty the Gauss orthogonal ensemble distribution. In the same model,the average value of the ratio of the adjacent gap in the critical state was identical.