Random Matrices with Correlated Elements: A Model for Disorder with Interactions

Details Random Matrices with Correlated Elements: A Model for Disorder with Interactions Random Matrices with Correlated Elements: A Model for Disorder with Interactions

2004-02-19

arxiv.org/abs/cond-mat/0402506v2

Phys. Rev. E, 71, 026226, (2005)

Physics

Condensed Matter

Disordered Systems and Neural Networks

19 Pages, No Figures, Major Changes to Explain the Mathematical Details

Scientific paper

10.1103/PhysRevE.71.026226

The complicated interactions in presence of disorder lead to a correlated randomization of states. The Hamiltonian as a result behaves like a multi-parametric random matrix with correlated elements. We show that the eigenvalue correlations of these matrices can be described by the single parametric Brownian ensembles. The analogy helps us to reveal many important features of the level-statistics in interacting systems e.g. a critical point behavior different from that of non-interacting systems, the possibility of extended states even in one dimension and a universal formulation of level correlations.

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