Chinese Physics B

Filling dependence of correlation exponents and metal-Mott insulator transition in strongly correlated electron systems

Ming-Xi Lin, SHeng-Wen Qi

Published Dec 1, 2010• 0 citations

Abstract

Using a universal relation between electron filling factor and ground state energy, this paper studies the dependence of correlation exponents on the electron filling factor of one-dimensional extended Hubbard model in a strong coupling regime, and demonstrates that in contrast to the usual Hubbard model ( g c = 1/2), the dimensionless coupling strength parameter g c heavily depends on the electron filling, and it has a "particle-hole" symmetry about electron quarter filling point. As increasing the nearest neighbouring repulsive interaction, the single particle spectral weight is transferred from low energy to high energy regimes. Moreover, at electron quarter filling, there is a metal-Mott insulator transition at the strong coupling point g c = 1/4, and this transition is a continuous phase transition.

DOI: 10.1088/1674-1056/19/12/127401

Related papers

Correlation exponents and the metal-insulator transition in the one-dimensional Hubbard model

Heinz J. Schulz

Physical Review LettersJun 4, 1990652 citations

Critical behavior near the metal-insulator transition in the one-dimensional extended Hubbard model at quarter filling

Kazuhiro Sano, Yūichi Ono

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

Effects of Strong Correlation and Randomness in the Vicinity of the Mott Transition in the Quasi-One-Dimensional Hubbard Model

Satoshi Fujimoto

arXiv:cond-mat/9910069Journal of the Physical Society of JapanAug 15, 20002 citations

Critical Properties of the Mott Transition in the Hubbard Model

Goetz Moeller, Qimiao Si A, Gabriel Kotliar +1 more

We introduce a systematic low-energy approach to strongly correlated electron systems in infinite dimensions, and apply it to the problem of the correlation-induced metal-insulator transition in the half-filled Hubbard model. We determine the low-energy scaling functions of the metallic state, including the single-particle Green function and dynamical spin susceptibility, as well as thermodynamic properties and relate them to experimental data in transition metal oxides.

arXiv:cond-mat/9402047Feb 10, 19940 citations

Mott-Hubbard phase transition in 2D electron liquid

Igor N. Karnaukhov, Kateryna Levchuk, Igor N. Dubinski

arXiv:2109.07550Sep 15, 20210 citations

Exact result on the Mott transition in a two-dimensional model of strongly correlated electrons

Frédéric Mila

arXiv:cond-mat/9404013Physical review. B, Condensed matterMay 15, 199410 citations

Chinese Physics B

Filling dependence of correlation exponents and metal-Mott insulator transition in strongly correlated electron systems

Ming-Xi Lin, SHeng-Wen Qi

Published Dec 1, 2010• 0 citations

Publisher

Abstract

DOI: 10.1088/1674-1056/19/12/127401

Related papers

Correlation exponents and the metal-insulator transition in the one-dimensional Hubbard model

Heinz J. Schulz

The long-distance decay of correlation functions in the one-dimensional Hubbard model is determined for arbitrary band filling and correlation strength, using the exact solution of Lieb and Wu. In particular, for either infinitely strong on-site repulsion U, or in the close proximity of half filling for any U, spin-spin correlations decay like cos(2 ${\mathit{k}}_{\mathit{F}}$ x)${\mathit{x}}^{\mathrm{\ensuremath{-}}3/2}$ ${\mathrm{ln}}^{1/2}$ (x). For infinite U the results are generalized to the case of nonzero nearest-neighbor interaction. The behavior of the frequency-dependent conductivity is also discussed, in particular in the proximity of the metal-insulator transitions occurring for half and quarter filling.The long-distance decay of correlation functions in the one-dimensional Hubbard model is determined for arbitrary band filling and correlation strength, using the exact solution of Lieb and Wu. In particular, for either infinitely strong on-site repulsion U, or in the close proximity of half filling for any U, spin-spin correlations decay like cos(2${\mathit{k}}_{\mathit{F}}$x)${\mathit{x}}^{\mathrm{\ensuremath{-}}3/2}$ ${\mathrm{ln}}^{1/2}$(x). For infinite U the results are generalized to the case of nonzero nearest-neighbor interaction. The behavior of the frequency-dependent conductivity is also discussed, in particular in the proximity of the metal-insulator transitions occurring for half and quarter filling.

Physical Review LettersJun 4, 1990652 citations

Critical behavior near the metal-insulator transition in the one-dimensional extended Hubbard model at quarter filling

Kazuhiro Sano, Yūichi Ono

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

Effects of Strong Correlation and Randomness in the Vicinity of the Mott Transition in the Quasi-One-Dimensional Hubbard Model

Satoshi Fujimoto

We study the strong correlation effects in the vicinity of the Mott metal-insulator transition using coupled clean or disordered Hubbard chains with a infinitely large coordinate number $D_{\perp}\to\infty$ in the direction perpendicular to the chains and with a long-range transverse hopping. Strong electron correlation effects are treated partially non-perturbatively with the use of the exact results for the 1D Hubbard model. In the case of clean systems, the thermodynamic and transport quantities which characterize the Mott transition from the Fermi liquid state, such as the specific heat coefficient, the Drude weight, and the compressibility, are obtained as functions of hole-doping $δ=1-n$ ( $n$ , electron density) by the systematic expansion in terms of the inverse of the transverse hopping range $l_{\perp}$ . We find that the $δ$ -dependence of these quantities shows non-universal behaviors with exponents depending on the strength of electron-electron interaction. In the presence of disorder, it is shown that the frequency-dependence of the dynamical conductivity obeys the Mott's law, implying the possibility of {\it Mott glass state} for $δ\to 0$ , provided that there exists a finite range interaction.We study the strong correlation effects in the vicinity of the Mott metal-insulator transition using coupled clean or disordered Hubbard chains with a infinitely large coordinate number $D_{\perp}\to\infty$ in the direction perpendicular to the chains and with a long-range transverse hopping. Strong electron correlation effects are treated partially non-perturbatively with the use of the exact results for the 1D Hubbard model. In the case of clean systems, the thermodynamic and transport quantities which characterize the Mott transition from the Fermi liquid state, such as the specific heat coefficient, the Drude weight, and the compressibility, are obtained as functions of hole-doping $δ=1-n$ ($n$, electron density) by the systematic expansion in terms of the inverse of the transverse hopping range $l_{\perp}$. We find that the $δ$-dependence of these quantities shows non-universal behaviors with exponents depending on the strength of electron-electron interaction. In the presence of disorder, it is shown that the frequency-dependence of the dynamical conductivity obeys the Mott's law, implying the possibility of {\it Mott glass state} for $δ\to 0$, provided that there exists a finite range interaction.

arXiv:cond-mat/9910069Journal of the Physical Society of JapanAug 15, 20002 citations

Critical Properties of the Mott Transition in the Hubbard Model

Goetz Moeller, Qimiao Si A, Gabriel Kotliar +1 more

arXiv:cond-mat/9402047Feb 10, 19940 citations

Mott-Hubbard phase transition in 2D electron liquid

Igor N. Karnaukhov, Kateryna Levchuk, Igor N. Dubinski

We study the behavior of fermion liquid defined on hexagonal and triangular lattices with short-range repulsion at half filling. In strong coupling limit the Mott-Hubbard phase state is present, the main peculiarity of insulator state is a doubled cell of the lattices. In the insulator state at half filling fermions with momenta $k$ and $k+π$ are coupled via the effective $λ$ -field, the gap in the spectrum of quasi-particle excitations opens and the Mott phase transition is occured at a critical value of the one-site Hubbard repulsion~ $U_c$ . $U_c=3.904$ and $U_c=5.125$ are calculated values for hexagonal and triangular lattices, respectively. Depending on the magnitude of the short-range repulsion, the gap in the spectrum and the energy of the ground state are calculated. The proposed approach is universal; it is implemented for an arbitrary dimension and symmetry of the lattice for fermions models with short-range repulsion.We study the behavior of fermion liquid defined on hexagonal and triangular lattices with short-range repulsion at half filling. In strong coupling limit the Mott-Hubbard phase state is present, the main peculiarity of insulator state is a doubled cell of the lattices. In the insulator state at half filling fermions with momenta $k$ and $k+π$ are coupled via the effective $λ$-field, the gap in the spectrum of quasi-particle excitations opens and the Mott phase transition is occured at a critical value of the one-site Hubbard repulsion~$U_c$. $U_c=3.904$ and $U_c=5.125$ are calculated values for hexagonal and triangular lattices, respectively. Depending on the magnitude of the short-range repulsion, the gap in the spectrum and the energy of the ground state are calculated. The proposed approach is universal; it is implemented for an arbitrary dimension and symmetry of the lattice for fermions models with short-range repulsion.

arXiv:2109.07550Sep 15, 20210 citations

Exact result on the Mott transition in a two-dimensional model of strongly correlated electrons

Frédéric Mila

We study the properties of a quarter-filled system of electrons on a square lattice interacting through a local repulsion U and a nearest-neighbor repulsion V in the limit V=+\ensuremath{\infty}. We identify the ground state for U large enough and show that domain walls appear below a critical value ${\mathit{U}}_{\mathit{c}}$ =4t/\ensuremath{\pi}. We argue that this corresponds to a metal-insulator transition due to Mott localization.We study the properties of a quarter-filled system of electrons on a square lattice interacting through a local repulsion U and a nearest-neighbor repulsion V in the limit V=+\ensuremath{\infty}. We identify the ground state for U large enough and show that domain walls appear below a critical value ${\mathit{U}}_{\mathit{c}}$=4t/\ensuremath{\pi}. We argue that this corresponds to a metal-insulator transition due to Mott localization.

arXiv:cond-mat/9404013Physical review. B, Condensed matterMay 15, 199410 citations

{\mathit{k}}_{\mathit{F}}

x)${\mathit{x}}^{\mathrm{\ensuremath{-}}3/2}$

{\mathrm{ln}}^{1/2}

(x). For infinite U the results are generalized to the case of nonzero nearest-neighbor interaction. The behavior of the frequency-dependent conductivity is also discussed, in particular in the proximity of the metal-insulator transitions occurring for half and quarter filling.

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 study the strong correlation effects in the vicinity of the Mott metal-insulator transition using coupled clean or disordered Hubbard chains with a infinitely large coordinate number

D_{\perp}\to\infty

in the direction perpendicular to the chains and with a long-range transverse hopping. Strong electron correlation effects are treated partially non-perturbatively with the use of the exact results for the 1D Hubbard model. In the case of clean systems, the thermodynamic and transport quantities which characterize the Mott transition from the Fermi liquid state, such as the specific heat coefficient, the Drude weight, and the compressibility, are obtained as functions of hole-doping

δ=1-n

(

n

, electron density) by the systematic expansion in terms of the inverse of the transverse hopping range

l_{\perp}

. We find that the

δ

-dependence of these quantities shows non-universal behaviors with exponents depending on the strength of electron-electron interaction. In the presence of disorder, it is shown that the frequency-dependence of the dynamical conductivity obeys the Mott's law, implying the possibility of {\it Mott glass state} for

δ\to 0

, provided that there exists a finite range interaction.

k

and

k+π

are coupled via the effective

λ

-field, the gap in the spectrum of quasi-particle excitations opens and the Mott phase transition is occured at a critical value of the one-site Hubbard repulsion~

U_c

U_c=3.904

and

U_c=5.125

are calculated values for hexagonal and triangular lattices, respectively. Depending on the magnitude of the short-range repulsion, the gap in the spectrum and the energy of the ground state are calculated. The proposed approach is universal; it is implemented for an arbitrary dimension and symmetry of the lattice for fermions models with short-range repulsion.

{\mathit{U}}_{\mathit{c}}

=4t/\ensuremath{\pi}. We argue that this corresponds to a metal-insulator transition due to Mott localization.