Comparisons of diagonal and off-diagonal Anderson localization using a random matrix model

We conduct a detailed study of Anderson localization in 1D and 2D disordered networks in a random matrix framework. Additionally, we analyze 2D networks with randomly broken links, which we interpret as networks with non-integer dimensions between 1D and 2D. We conduct our extensive numerical analysis for both diagonal and off-diagonal disorder. In particular, we compute the localization length's probability density function using two different metrics, one using the standard deviation and another using the inverse participation ratio. Both methods gauge the spread of eigenvectors over the matrix's element space. The probability density function provides the maximum amount of information regarding the localization, quite more than just the mean localization length. In particular, it allows us to clearly differentiate the localization process for the diagonal versus the off-diagonal disorder. It also allows us to compare the behavior of the two metrics.

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