TY - JOUR

T1 - Statistics of Hartree-Fock levels in small disordered systems

AU - Levit, Shimon

AU - Orgad, Dror

PY - 1999

Y1 - 1999

N2 - We study the statistics of quasiparticle and quasihole levels in small interacting disordered systems within the Hartree-Fock approximation. The distribution of the inverse compressibility, given according to Koopmans’ theorem by the distance between the two levels across the Fermi energy, evolves from a Wigner distribution in the noninteracting limit to a shifted Gaussian for strong interactions. On the other hand, the nature of the distribution of spacings between neighboring levels on the same side of the Fermi energy (corresponding to energy differences between excited states of the system with one missing or one extra electron) is not affected by the interaction and follows Wigner-Dyson statistics. These results are derived analytically by isolating and solving the appropriate Hartree-Fock equations for the two levels. They are substantiated by numerical simulations of the full set of Hartree-Fock equations for a disordered quantum dot with Coulomb interactions. We find enhanced fluctuations of the inverse compressibility compared to the prediction of the random matrix theory, possibly due to the localization of the wave functions around the edge of the dot. The distribution of the inverse compressibility calculated from the discrete second derivative with respect to the number of particles of the Hartree-Fock ground state energy deviates from the distribution of the level spacing across the Fermi energy. The two distributions have similar shapes but are shifted with respect to each other. The deviation increases with the strength of the interaction thus indicating the breakdown of Koopmans’ theorem in the strongly interacting limit.

AB - We study the statistics of quasiparticle and quasihole levels in small interacting disordered systems within the Hartree-Fock approximation. The distribution of the inverse compressibility, given according to Koopmans’ theorem by the distance between the two levels across the Fermi energy, evolves from a Wigner distribution in the noninteracting limit to a shifted Gaussian for strong interactions. On the other hand, the nature of the distribution of spacings between neighboring levels on the same side of the Fermi energy (corresponding to energy differences between excited states of the system with one missing or one extra electron) is not affected by the interaction and follows Wigner-Dyson statistics. These results are derived analytically by isolating and solving the appropriate Hartree-Fock equations for the two levels. They are substantiated by numerical simulations of the full set of Hartree-Fock equations for a disordered quantum dot with Coulomb interactions. We find enhanced fluctuations of the inverse compressibility compared to the prediction of the random matrix theory, possibly due to the localization of the wave functions around the edge of the dot. The distribution of the inverse compressibility calculated from the discrete second derivative with respect to the number of particles of the Hartree-Fock ground state energy deviates from the distribution of the level spacing across the Fermi energy. The two distributions have similar shapes but are shifted with respect to each other. The deviation increases with the strength of the interaction thus indicating the breakdown of Koopmans’ theorem in the strongly interacting limit.

UR - http://www.scopus.com/inward/record.url?scp=0000164554&partnerID=8YFLogxK

U2 - 10.1103/PhysRevB.60.5549

DO - 10.1103/PhysRevB.60.5549

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AN - SCOPUS:0000164554

SN - 1098-0121

VL - 60

SP - 5549

EP - 5560

JO - Physical Review B - Condensed Matter and Materials Physics

JF - Physical Review B - Condensed Matter and Materials Physics

IS - 8

ER -