Localization and absence of Breit-Wigner form for Cauchy random band matrices
Frahm, Klaus M.
Original · EN
We analytically calculate the local density of states for Cauchy random band matrices with strongly fluctuating diagonal elements. The Breit-Wigner form for ordinary band matrices is replaced by a Levy distribution of index μ=1/2 and the characteristic energy scale α is strongly enhanced as compared to the Breit-Wigner width. The unperturbed eigenstates decay according to the non-exponential law ∝ e-√αt. We analytically determine the localization length by a new method to derive the supersymmetric non-linear σ model for this type of band matrices.
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