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

Kazuhiro Sano·Yoshiaki Ono
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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 $K_ρ$ which is substituted into the renormalization group equation as an initial condition. It leads $K_ρ$ 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.

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Kazuhiro Sano, Yoshiaki Ono. 2004-04-29. Combined Analysis of Numerical Diagonalization and Renormalization Group methods for the One-Dimensional $U$-$V$ Model at Quarter filling. https://doi.org/10.1103/physrevb.70.155102

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