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arXiv:cond-mat/0304245 · Physical review. B, Condensed matter

Statistical properties of the first excited state of an interacting many-particle disordered system

Richard Berkovits, Yuval Gefen, Igor V. Lerner, B. L. Altshuler

Published Aug 14, 2003• 9 citations
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Abstract

The distribution ${P}_{1}$ of the first many-body excitation energy of a weakly and moderately interacting electron gas in a finite conductor (in the diffusive regime) is calculated. As the interaction is increased, ${P}_{1}$ crosses over from Wigner-Dyson to Poisson distributions. We characterize this transition through the inverse participation ratio in Hilbert space, and examine its manifestation in a projected two-dimensional space.

DOI
10.1103/physrevb.68.085314

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The distribution P1{P}_{1}P1​ of the first many-body excitation energy of a weakly and moderately interacting electron gas in a finite conductor (in the diffusive regime) is calculated. As the interaction is increased, P1{P}_{1}P1​ crosses over from Wigner-Dyson to Poisson distributions. We characterize this transition through the inverse participation ratio in Hilbert space, and examine its manifestation in a projected two-dimensional space.
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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 = Δc, but also by the ratio Δc = δ. V is the typical interaction matrix element, δ is the energy distance between many-body states and Δc is the distance between many-body states coupled by the interaction.
The energy level separation distribution of a fermionic disordered many-particle system is studied. For a non-interacting system, a crossover is observed from a Wigner (GOE) distribution for the first and second excitations to a different form which depends on the number of particles for low-lying excitations and then to a Poisson distribution for high excitations. This behaviour also holds for weakly interacting systems, while for stronger interactions a transition of the high excitations to a Wigner distribution is observed.
We study the level spacing statistics P(s)P(s)P(s) and eigenstate properties of spinless fermions with Coulomb interaction on a two-dimensional lattice at constant filling factor and various disorder strengths. For the noninteracting localized phase in the limit of large lattice size, Coulomb interaction induces a transition of P(s)P(s)P(s) from the Poisson to the Wigner-Dyson distribution, at a critical total energy independent of the number of fermions. This implies the emergence of quantum ergodicity induced by interaction and delocalization in the Hilbert space at zero temperature inside the one-particle insulating phase.
The level statistics of a tight-binding Hamiltonian describing strongly interacting particles in a disordered system is investigated. It is found to be characterized by two transitions as functions of interaction strength. The first is from Poisson statistics to Wigner (GOE) statistics as interactions between the particles are turned on, and the second is back to Poisson statistics as the interactions become stronger. The dependences of both transitions on the interaction strength, filling factor, size of the sample, disorder and range of interactions are considered. Possible experimental consequences are discussed.
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 many‐body states and Δ c is the distance between many‐body states coupled by the interaction.