Single-particle excitations under coexisting electron correlation and disorder: A numerical study of the anderson-hubbard model

Hiroshi Shinaoka*, Masatoshi Imada

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

45 Citations (Scopus)


Interplay of electron correlation and randomness is studied using the Anderson-Hubbard model within the Hartree-Fock (HF) approximation. Under the coexistence of short-range interaction and diagonal disorder, we obtain the ground-state phase diagram in three dimensions (3D), which includes an antiferromagnetic insulator, an antiferromagnetic metal, a paramagnetic insulator (Anderson-localized insulator), and a paramagnetic metal. Although only the short-range interaction is present in this model, we find unconventional soft gaps in the insulating phases irrespective of electron filling, spatial dimensions, and long-range order, where the single-particle density of states (DOS) vanishes with a power-law scaling in 1D or even faster in 2D and 3D toward the Fermi energy. We call such a gap a soft Hubbard gap. Moreover, exact-diagonalization results for 1D support the formation of a soft Hubbard gap beyond the mean-field level. The formation of the soft Hubbard gap cannot be attributed to the conventional theory by Efros and Shklovskii (ES) owing the emergence of soft gaps to the long-range Coulomb interaction. Indeed, on the basis of a multivalley energy landscape, we propose a phenomenological scaling theory, which predicts a scaling of the DOS, A in energy E as A(E) α exp[γlog |E- Ej|d. Here, d is the spatial dimension, EF is the Fermi energy, and γ is a non universal constant. This scaling is in perfect agreement with the numerical results. We further discuss a correction of the scaling of the DOS by the long-range part of the Coulomb interaction, which modifies the ES scaling. Furthermore, explicit formulae for the temperature dependence of the DC resistivity via variable-range hopping under the influence of the soft gaps are derived. Finally, we compare the present theory with experimental results for SrRu1-xTi xO3.

Original languageEnglish
Article number094708
Journaljournal of the physical society of japan
Issue number9
Publication statusPublished - 2009 Sept
Externally publishedYes


  • Anderson-hubbard model
  • Disorder
  • Electron correlation
  • Single-particle density of states
  • Soft gap
  • Variable-range hopping

ASJC Scopus subject areas

  • Physics and Astronomy(all)


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