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TT: Tiefe Temperaturen
TT 6: Postersitzung I: Josephsonkontakte und SQUIDs, Supraleitung: Theorie, Korrelierte Elektronen, Niederdimensionale Systeme, Magnetotransport, Quantenhalleffekt, Kohlenstoff-Nanoröhrchen, Quantenflüssigkeiten
TT 6.24: Poster
Monday, March 26, 2001, 14:30–17:00, Rang S\ 3
Mott–Hubbard insulators in the limit of strong coupling:density of states in one and infinite dimensions — •Eva Kalinowski and Florian Gebhard — Fachbereich Physik, Philipps-Universität Marburg
Starting from Takahashi’s t/U expansion [1] for the half-filled Hubbard model, we calculate the density of states on a Bethe lattice for coordination numbers Z=2 (one dimension) and Z→∞ (limit of infinite dimensions).
In one dimension, we reproduce the exact gap Δ(U/t) [2] to second order in the expansion parameter (t/U). In the limit of infinite dimensions, we find Δ(U/t)=U−W+W2/(16 U) + … for a spin-disordered ground state, where W=4t is the width of the non-interacting density of states. This result indicates that t/U corrections to the gap are small down to the Mott–Hubbard transition at Uc≈ W, in agreement with numerical results from the Random Dispersion Approximation [3].
[1] M. Takahashi, J. Phys. C 10, 1289 (1977).
[2] E.H. Lieb and F.Y. Wu, Phys. Rev. Lett. 20, 1445 (1968).
[3] R.M. Noack and F. Gebhard, Phys. Rev. Lett. 82, 1915 (1999).