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Journal of Physics Condensed Matter

The excitation statistics of disordered strongly correlated systems

Richard Berkovits, Y. Avishai

Published Jan 22, 1996• 21 citations
Publisher

Abstract

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.

DOI
10.1088/0953-8984/8/4/006

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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.
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The effect of Coulomb and short-range interactions on the spectral properties of two-dimensional disordered systems with two spinless fermions is investigated by numerical scaling techniques. The size independent universality of the critical nearest-level-spacing distribution P(s)P(s)P(s) allows one to find a delocalization transition at a critical disorder Wc{W}_{\mathrm{c}}Wc​ for any nonzero value of the interaction strength. At the critical point the spacings distribution has a small- sss behavior ${P}_{c}(s)\ensuremath{\propto}s$, and a Poisson-like decay at large spacings.