Distribution of the local density of states as a criterion for Anderson localization: Numerically exact results for various lattices in two and three dimensions

Details Distribution of the local density of states as a criterion for Anderson localization: Numerically exact results for various lattices in two and three dimensions Distribution of the local density of states as a criterion for Anderson localization: Numerically exact results for various lattices in two and three dimensions

2010-02-15

arxiv.org/abs/1002.2895v2

Phys. Rev. B 81, 155106 (2010)

Physics

Condensed Matter

Strongly Correlated Electrons

extended version, new appendix A added, 9 pages, 8 figures

Scientific paper

Numerical approaches to Anderson localization face the problem of having to treat large localization lengths while being restricted to finite system sizes. We show that by finite-size scaling of the probability distribution of the local density of states (LDOS) this long-standing problem can be overcome. To this end we reexamine the approach, propose numerical refinements, and apply it to study the dependence of the distribution of the LDOS on the dimensionality and coordination number of the lattice. Particular attention is given to the graphene lattice. We show that the system-size dependence of the LDOS distribution is indeed an unambiguous sign of Anderson localization, irrespective of the dimension and lattice structure. The numerically exact LDOS data obtained by us agree with a log-normal distribution over up to ten orders of magnitude and thereby fulfill a nontrivial symmetry relation previously derived for the non-linear $\sigma$-model.

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