Combined Analysis of Numerical Diagonalization and Renormalization Group methods for the One-Dimensional $U$-$V$ Model at Quarter filling

Abstract

The one-dimensional extended Hubbard model with both the on-site $U$ and the nearest neighbor $V$ interactions at quarter filling is studied by using a novel finite size scaling. We diagonalize finite size systems numerically and calculate the Luttinger-liquid parameter $K_{\rho }$ which is substituted into the renormalization group equation as an initial condition. It leads $K_{\rho }$ in the infinite size system and the result agrees very well with the available exact result with $U=\infty$. This approach also yields the charge gap in the insulating state near the metal-insulator transition where the characteristic energy becomes exponentially small and the usual finite size scaling is not applicable.

7 pages, 8 figures,submitted to PRB

References in corpus (8)

• One-Dimensional Fermi liquids
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• Phase diagram of the one-dimensional extended Hubbard model with attractive and/or repulsive interactions at quarter filling
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