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Many-body spectral statistics of interacting Fermions

M. Pascaud·G. Montambaux
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Abstract

We have studied the appearance of chaos in the many-body spectrum of interacting Fermions. The coupling of a single state to the Fermi sea is considered. This state is coupled to a hierarchy of states corresponding to one or several particle-hole excitations. We have considered various couplings between two successive generations of this hierarchy and determined under which conditions this coupling can lead to Wigner-Dyson correlations. We have found that the cross-over from a Poisson to a Wigner distribution is characterized not only by the ratio $V/Δ_c$, but also by the ratio $Δ_c/δ$. $V$ is the typical interaction matrix element, $δ$ is the energy distance between {\it many-body} states and $Δ_c$ is the distance between many-body states coupled by the interaction.

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M. Pascaud, G. Montambaux. 1998-10-17. Many-body spectral statistics of interacting Fermions. https://doi.org/10.1002/(sici)1521-3889(199811)7%3A5%2F6%3C406%3A%3Aaid-andp406%3E3.0.co%3B2-d

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