2004/01/31 by Kazuhiro Sano, Yoshiaki Ono, Yūichi Ono · 1 citation
Mathematics · Physics and Astronomy · #Condensed matter physics #Electrical resistivity and conductivity #Geometry #Hubbard model #Mathematical physics #Mathematics #Metal–insulator transition #Physics #Physics of Superconductivity and Magnetism #Quantum and electron transport phenomena #Quantum many-body systems #Quantum mechanics #Renormalization group #Scaling #Statistical physics #Superconductivity #cond-mat.str-el
paper · pdf · doi:10.1103/physrevb.70.155102
published as Phys. Rev. B70, 155102 (2004) · 7 pages, 8 figures,submitted to PRB
arxiv created 2004/04/29 · openalex publication_date 2004/10/06 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
We examine the critical behavior near the metal-insulator transition (MIT) in the one-dimensional extended Hubbard model with the on-site and the nearest-neighbor interactions U and V at quarter filling using a combined method of the numerical diagonalization and the renormalization group (RG). The Luttinger-liquid parameter K_\ensuremathρ is calculated with the exact diagonalization for finite size systems and is substituted into the RG equation as an initial condition to obtain K_\ensuremathρ in the infinite size system. This approach also yields the charge gap \ensuremathΔ in the insulating state near the MIT. The results agree very well with the available exact results for U=\ensuremath∞ even in the critical regime of the MIT where the characteristic energy becomes exponentially small and the usual finite size scaling is not applicable. When the system approaches the MIT critical point V\ensuremath→Vc for a fixed U, K_\ensuremathρ and \ensuremathΔ behave as \ensuremath|ln\ensuremathΔ\ensuremath|^\ensuremath-2=c_\ensuremathΔ(V∕Vc\ensuremath-1) and (K_\ensuremathρ\ensuremath-1∕4)2=cK(1\ensuremath-V∕Vc), where the critical value Vc and the coefficients c_\ensuremathΔ and cK are functions of U. These critical properties, which are known to be exact for U=\ensuremath∞, are observed also for finite U case. We also observe the same critical behavior in the limit of the MIT critical point U\ensuremath→Uc when U is varied for a fixed V.