Orthogonality Catastrophe in Parametric Random Matrices

Details Orthogonality Catastrophe in Parametric Random Matrices Orthogonality Catastrophe in Parametric Random Matrices

2001-06-29

arxiv.org/abs/cond-mat/0106640v1

Physics

Condensed Matter

Mesoscale and Nanoscale Physics

12 pages, 8 figures

Scientific paper

10.1103/PhysRevB.65.085309

We study the orthogonality catastrophe due to a parametric change of the single-particle (mean field) Hamiltonian of an ergodic system. The Hamiltonian is modeled by a suitable random matrix ensemble. We show that the overlap between the original and the parametrically modified many-body ground states, $S$, taken as Slater determinants, decreases like $n^{-k x^2}$, where $n$ is the number of electrons in the systems, $k$ is a numerical constant of the order of one, and $x$ is the deformation measured in units of the typical distance between anticrossings. We show that the statistical fluctuations of $S$ are largely due to properties of the levels near the Fermi energy.

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