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 ${K}_{\ensuremath{\rho}}$ is calculated with the exact diagonalization for finite size systems and is substituted into the RG equation as an initial condition to obtain ${K}_{\ensuremath{\rho}}$ in the infinite size system. This approach also yields the charge gap $\ensuremath{\Delta}$ in the insulating state near the MIT. The results agree very well with the available exact results for $U=\ensuremath{\infty}$ 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 $V\ensuremath{\rightarrow}{V}_{c}$ for a fixed $U$ , ${K}_{\ensuremath{\rho}}$ and $\ensuremath{\Delta}$ behave as ${\ensuremath{\mid}\mathrm{l}\mathrm{n}\ensuremath{\Delta}\ensuremath{\mid}}^{\ensuremath{-}2}={c}_{\ensuremath{\Delta}}(V∕{V}_{c}\ensuremath{-}1)$ and ${({K}_{\ensuremath{\rho}}\ensuremath{-}1∕4)}^{2}={c}_{K}(1\ensuremath{-}V∕{V}_{c})$, where the critical value ${V}_{c}$ and the coefficients ${c}_{\ensuremath{\Delta}}$ and ${c}_{K}$ are functions of $U$ . These critical properties, which are known to be exact for $U=\ensuremath{\infty}$, are observed also for finite $U$ case. We also observe the same critical behavior in the limit of the MIT critical point $U\ensuremath{\rightarrow}{U}_{c}$ when $U$ is varied for a fixed $V$ .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 ${K}_{\ensuremath{\rho}}$ is calculated with the exact diagonalization for finite size systems and is substituted into the RG equation as an initial condition to obtain ${K}_{\ensuremath{\rho}}$ in the infinite size system. This approach also yields the charge gap $\ensuremath{\Delta}$ in the insulating state near the MIT. The results agree very well with the available exact results for $U=\ensuremath{\infty}$ 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 $V\ensuremath{\rightarrow}{V}_{c}$ for a fixed $U$, ${K}_{\ensuremath{\rho}}$ and $\ensuremath{\Delta}$ behave as ${\ensuremath{\mid}\mathrm{l}\mathrm{n}\ensuremath{\Delta}\ensuremath{\mid}}^{\ensuremath{-}2}={c}_{\ensuremath{\Delta}}(V∕{V}_{c}\ensuremath{-}1)$ and ${({K}_{\ensuremath{\rho}}\ensuremath{-}1∕4)}^{2}={c}_{K}(1\ensuremath{-}V∕{V}_{c})$, where the critical value ${V}_{c}$ and the coefficients ${c}_{\ensuremath{\Delta}}$ and ${c}_{K}$ are functions of $U$. These critical properties, which are known to be exact for $U=\ensuremath{\infty}$, are observed also for finite $U$ case. We also observe the same critical behavior in the limit of the MIT critical point $U\ensuremath{\rightarrow}{U}_{c}$ when $U$ is varied for a fixed $V$.

arXiv:cond-mat/0401256Physical Review BOct 6, 200417 citations

Quantum metal-insulator transition at half-filling

Hsueh‐Ju Lin, Chunchun Wu

Synthetic MetalsMar 1, 20011 citation

Charge gap in the one-dimensional extended Hubbard model at quarter filling

Kazuhiro Sano, Yūichi Ono

We propose a different combined approach, which consists of the exact diagonalization, renormalization group, and Bethe ansatz methods, for precise estimates of the charge gap $\ensuremath{\Delta}$ in the one-dimensional extended Hubbard model, with on-site and nearest-neighbor interactions $U$ and $V$ at quarter filling. This approach enables us to obtain the absolute value of $\ensuremath{\Delta}$, including the prefactor, without ambiguity even in the critical regime of the metal-insulator transition (MIT) where $\ensuremath{\Delta}$ is exponentially small, beyond usual renormalization group methods and/or finite-size scaling approaches. The detailed results of $\ensuremath{\Delta}$, down to the order of ${10}^{\ensuremath{-}10}$ near the MIT, are shown as contour lines on the $U\text{\ensuremath{-}}V$ plane.We propose a different combined approach, which consists of the exact diagonalization, renormalization group, and Bethe ansatz methods, for precise estimates of the charge gap $\ensuremath{\Delta}$ in the one-dimensional extended Hubbard model, with on-site and nearest-neighbor interactions $U$ and $V$ at quarter filling. This approach enables us to obtain the absolute value of $\ensuremath{\Delta}$, including the prefactor, without ambiguity even in the critical regime of the metal-insulator transition (MIT) where $\ensuremath{\Delta}$ is exponentially small, beyond usual renormalization group methods and/or finite-size scaling approaches. The detailed results of $\ensuremath{\Delta}$, down to the order of ${10}^{\ensuremath{-}10}$ near the MIT, are shown as contour lines on the $U\text{\ensuremath{-}}V$ plane.

arXiv:cond-mat/0612050Physical Review BMar 12, 200710 citations

Metal—insulator transition in one-dimensional metals

H. Heyszenau

Solid State CommunicationsJan 1, 19763 citations

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 ${K}_{\ensuremath{\rho}}$ is calculated with the exact diagonalization for finite size systems and is substituted into the RG equation as an initial condition to obtain ${K}_{\ensuremath{\rho}}$ in the infinite size system. This approach also yields the charge gap $\ensuremath{\Delta}$ in the insulating state near the MIT. The results agree very well with the available exact results for $U=\ensuremath{\infty}$ 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 $V\ensuremath{\rightarrow}{V}_{c}$ for a fixed

U

, ${K}_{\ensuremath{\rho}}$ and $\ensuremath{\Delta}$ behave as ${\ensuremath{\mid}\mathrm{l}\mathrm{n}\ensuremath{\Delta}\ensuremath{\mid}}^{\ensuremath{-}2}={c}_{\ensuremath{\Delta}}(V∕{V}_{c}\ensuremath{-}1)$ and ${({K}_{\ensuremath{\rho}}\ensuremath{-}1∕4)}^{2}={c}_{K}(1\ensuremath{-}V∕{V}_{c})$, where the critical value

{V}_{c}

and the coefficients ${c}_{\ensuremath{\Delta}}$ and

{c}_{K}

are functions of

U

. These critical properties, which are known to be exact for $U=\ensuremath{\infty}$, are observed also for finite

U

case. We also observe the same critical behavior in the limit of the MIT critical point $U\ensuremath{\rightarrow}{U}_{c}$ when

U

is varied for a fixed

V

U

and

V

at quarter filling. This approach enables us to obtain the absolute value of $\ensuremath{\Delta}$, including the prefactor, without ambiguity even in the critical regime of the metal-insulator transition (MIT) where $\ensuremath{\Delta}$ is exponentially small, beyond usual renormalization group methods and/or finite-size scaling approaches. The detailed results of $\ensuremath{\Delta}$, down to the order of ${10}^{\ensuremath{-}10}$ near the MIT, are shown as contour lines on the $U\text{\ensuremath{-}}V$ plane.