arXiv:cond-mat/0609049 · Physical Review B

Low-energy excitations of the one-dimensional half-filled SU(4) Hubbard model with an attractive on-site interaction: Density-matrix renormalization-group calculations and perturbation theory

Jize Zhao, Kazuo Ueda, Xiaoqun Wang

Published Dec 19, 2006• 12 citations

Abstract

We investigate low-energy excitations of the one-dimensional half-filled SU(4) Hubbard model with an attractive on-site interaction $U<0$ using the density-matrix renormalization-group method as well as perturbation theory. We find that the ground state is a charge-density-wave state with long-range order. The ground state is completely incompressible since all the excitations are gapful. The charge gap, which is the same as the four-particle excitation gap, is a nonmonotonic function of $U$, while the spin gap and others increase with increasing $\ensuremath{\mid}U\ensuremath{\mid}$ and have linear asymptotic behaviors.

DOI: 10.1103/physrevb.74.233102

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Insulating Charge Density Wave for a Half-Filled SU(N) Hubbard Model with an Attractive On-Site Interaction in One Dimension

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Mott transition and dimerization in the one-dimensional SU(n) Hubbard model

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arXiv:cond-mat/0609049 · Physical Review B

Low-energy excitations of the one-dimensional half-filled SU(4) Hubbard model with an attractive on-site interaction: Density-matrix renormalization-group calculations and perturbation theory

Jize Zhao, Kazuo Ueda, Xiaoqun Wang

Published Dec 19, 2006• 12 citations

arXiv HTML PDF

Abstract

We investigate low-energy excitations of the one-dimensional half-filled SU(4) Hubbard model with an attractive on-site interaction

U<0

using the density-matrix renormalization-group method as well as perturbation theory. We find that the ground state is a charge-density-wave state with long-range order. The ground state is completely incompressible since all the excitations are gapful. The charge gap, which is the same as the four-particle excitation gap, is a nonmonotonic function of

U

, while the spin gap and others increase with increasing

\ensuremath{\mid}U\ensuremath{\mid}

and have linear asymptotic behaviors.

DOI: 10.1103/physrevb.74.233102

Related papers

Insulating Charge Density Wave for a Half-Filled SU(N) Hubbard Model with an Attractive On-Site Interaction in One Dimension

Jize Zhao, Kazuo Ueda, Xiaoqun Wang

We study a one-dimensional SU(N) Hubbard model with an attractive on-site interaction and $N>2$ at half-filling on the bipartite lattice using density-matrix renormalization-group method and a perturbation theory. We find that the ground state of the SU(N) Hubbard model is a charge density wave state with two-fold degeneracy. All the excitations are found to be gapful, resulting in an insulating ground state, on contrary to that in the SU(2) case. Moreover, the charge gap is equal to the Cooperon gap, which behaves as $-2Nt^2/(N-1)U$ in the strong coupling regime. However, the spin gap $Δ_{s}$ and the quasiparticle gap $Δ_{1}$ as well open exponentially in the weak coupling region, while in the strong coupling region, they linearly depend on $U$ such that $Δ_{s}\sim -U(N-1)$ and $Δ_{1}\sim -U(N-1)/2$ .We study a one-dimensional SU(N) Hubbard model with an attractive on-site interaction and $N>2$ at half-filling on the bipartite lattice using density-matrix renormalization-group method and a perturbation theory. We find that the ground state of the SU(N) Hubbard model is a charge density wave state with two-fold degeneracy. All the excitations are found to be gapful, resulting in an insulating ground state, on contrary to that in the SU(2) case. Moreover, the charge gap is equal to the Cooperon gap, which behaves as $-2Nt^2/(N-1)U$ in the strong coupling regime. However, the spin gap $Δ_{s}$ and the quasiparticle gap $Δ_{1}$ as well open exponentially in the weak coupling region, while in the strong coupling region, they linearly depend on $U$ such that $Δ_{s}\sim -U(N-1)$ and $Δ_{1}\sim -U(N-1)/2$.

arXiv:cond-mat/0702582Journal of the Physical Society of JapanNov 12, 200713 citations

Mott transition and dimerization in the one-dimensional SU(n) Hubbard model

K. Buchta, Örs Legeza, E. Szirmai +1 more

The one-dimensional $\mathrm{SU}(n)$ Hubbard model is investigated numerically for $n=2$ , 3, 4, and 5 at half-filling and $1∕n$ filling using the density-matrix renormalization-group method. The energy gaps and various quantum information entropies are calculated. In the half-filled case, finite spin and charge gaps are found for arbitrary positive $U$ if $n>2$ . Furthermore, it is shown that the transition to the gapped phase at ${U}_{c}=0$ is of Kosterlitz-Thouless type and is accompanied by a bond dimerization both for even and odd $n$ . In the $1∕n$ -filled case, the transition has similar features as the metal-insulator transition in the half-filled SU(2) Hubbard model. The charge gap opens exponentially slowly for $U>{U}_{c}=0$ , the spin sector remains gapless, and the ground state is nondimerized.The one-dimensional $\mathrm{SU}(n)$ Hubbard model is investigated numerically for $n=2$, 3, 4, and 5 at half-filling and $1∕n$ filling using the density-matrix renormalization-group method. The energy gaps and various quantum information entropies are calculated. In the half-filled case, finite spin and charge gaps are found for arbitrary positive $U$ if $n>2$. Furthermore, it is shown that the transition to the gapped phase at ${U}_{c}=0$ is of Kosterlitz-Thouless type and is accompanied by a bond dimerization both for even and odd $n$. In the $1∕n$-filled case, the transition has similar features as the metal-insulator transition in the half-filled SU(2) Hubbard model. The charge gap opens exponentially slowly for $U>{U}_{c}=0$, the spin sector remains gapless, and the ground state is nondimerized.

arXiv:cond-mat/0607374Physical Review BApr 19, 200748 citations

Effect of Hund coupling in the one-dimensional SU(4) Hubbard model

Hyun Cheol Lee, P. Azaria, E. Boulat

The one-dimensional SU(4) Hubbard model perturbed by Hund coupling is studied, away from half-filling, by means of renormalization-group and bosonization methods. A spectral gap is always present in the spin-orbital sector irrespective of the magnitude of the Coulomb repulsion. We further distinguish between two qualitatively different regimes. At small Hund coupling, we find that the symmetry of the system is dynamically enlarged to SU(4) at low energy with the result of coherent spin-orbital excitations. When the charge sector is not gapped, a superconducting instability is shown to exist. At large Hund coupling, the symmetry is no longer enlarged to SU(4) and the excitations in the spin sector become incoherent. Furthermore, the superconductivity can be suppressed in favor of the conventional charge density wave state.The one-dimensional SU(4) Hubbard model perturbed by Hund coupling is studied, away from half-filling, by means of renormalization-group and bosonization methods. A spectral gap is always present in the spin-orbital sector irrespective of the magnitude of the Coulomb repulsion. We further distinguish between two qualitatively different regimes. At small Hund coupling, we find that the symmetry of the system is dynamically enlarged to SU(4) at low energy with the result of coherent spin-orbital excitations. When the charge sector is not gapped, a superconducting instability is shown to exist. At large Hund coupling, the symmetry is no longer enlarged to SU(4) and the excitations in the spin sector become incoherent. Furthermore, the superconductivity can be suppressed in favor of the conventional charge density wave state.

arXiv:cond-mat/0310003Physical Review BApr 15, 200427 citations

Phase Diagram of the One-Dimensional Half-Filled Extended Hubbard Model

Satoshi Ejima, Satoshi Nishimoto

We determine the ground-state phase diagram of the one-dimensional half-filled Hubbard model with on-site (nearest-neighbor) repulsive interaction U (V) and nearest-neighbor hopping t using the density-matrix renormalization group technique. Based on the results of the excitation gaps, Luttinger-liquid exponents, and bond-order-wave (BOW) order parameter, we confirm that the BOW phase appears in a substantial region between the charge-density-wave (CDW) and spin-density-wave phases. Each phase boundary is determined by multiple means and it allows us to make a cross-check on the validity of our estimations. We also find that the BOW-CDW transition changes from continuous to first order at the tricritical point (U(t),V(t)) approximately (5.89 t,3.10 t) and the BOW phase shrinks to zero at the critical end point (U(c),V(c)) approximately (9.25 t,4.76 t).We determine the ground-state phase diagram of the one-dimensional half-filled Hubbard model with on-site (nearest-neighbor) repulsive interaction U (V) and nearest-neighbor hopping t using the density-matrix renormalization group technique. Based on the results of the excitation gaps, Luttinger-liquid exponents, and bond-order-wave (BOW) order parameter, we confirm that the BOW phase appears in a substantial region between the charge-density-wave (CDW) and spin-density-wave phases. Each phase boundary is determined by multiple means and it allows us to make a cross-check on the validity of our estimations. We also find that the BOW-CDW transition changes from continuous to first order at the tricritical point (U(t),V(t)) approximately (5.89 t,3.10 t) and the BOW phase shrinks to zero at the critical end point (U(c),V(c)) approximately (9.25 t,4.76 t).

arXiv:0710.0673Physical Review LettersNov 20, 2007119 citations

Ground-State Phase Diagram of a Half-Filled One-Dimensional Extended Hubbard Model

Eric Jeckelmann

The density-matrix renormalization group is used to study the phase diagram of the one-dimensional half-filled Hubbard model with on-site (U) and nearest-neighbor (V) repulsion and hopping t. A critical line V(c)(U) approximately U/2 separates a Mott insulating phase from a charge-density-wave phase. The formation of bound charge excitations for V>2t changes the phase transition from continuous to first-order at a tricritical point U(t) approximately 3.7t, V(t)=2t. A frustrating effective antiferromagnetic spin coupling induces a bond-order-wave phase on the critical line V(c)(U) for U(t)<U less, similar 7t.The density-matrix renormalization group is used to study the phase diagram of the one-dimensional half-filled Hubbard model with on-site (U) and nearest-neighbor (V) repulsion and hopping t. A critical line V(c)(U) approximately U/2 separates a Mott insulating phase from a charge-density-wave phase. The formation of bound charge excitations for V>2t changes the phase transition from continuous to first-order at a tricritical point U(t) approximately 3.7t, V(t)=2t. A frustrating effective antiferromagnetic spin coupling induces a bond-order-wave phase on the critical line V(c)(U) for U(t)<U less, similar 7t.

arXiv:cond-mat/0204244Physical Review LettersNov 15, 2002133 citations

Renormalization group approach to the one-dimensional 1/4-filled Hubbard model with alternating on-site interactions

George Jackeli, Japaridze, G

The one-dimensional Hubbard model with different on-site interactions is investigated by renormalization group technique. In the case of a 1/4-filled band the dynamical nonequivalence of sites leads to the appearance of Umklapp processes in the system and to the dynamical generation of a gap in the charge excitation spectrum for $U_{a}\\not=U_{b}$ , $U_{a}>0$ or $U_{b}>0$ . The ground-state phase diagram is obtained in the limit of second order renormalization. Depending on the sign and relative values of the bare coupling constants, there is a gap in the spin or charge excitation spectrum and the model system tends to superconducting or antiferromagnetic order at T=0, with doubled period. The role of interaction between particles on nearest and next-nearest neighbor sites is also considered.The one-dimensional Hubbard model with different on-site interactions is investigated by renormalization group technique. In the case of a 1/4-filled band the dynamical nonequivalence of sites leads to the appearance of Umklapp processes in the system and to the dynamical generation of a gap in the charge excitation spectrum for $U_{a}\\not=U_{b}$, $U_{a}>0$ or $U_{b}>0$. The ground-state phase diagram is obtained in the limit of second order renormalization. Depending on the sign and relative values of the bare coupling constants, there is a gap in the spin or charge excitation spectrum and the model system tends to superconducting or antiferromagnetic order at T=0, with doubled period. The role of interaction between particles on nearest and next-nearest neighbor sites is also considered.

Jan 17, 19962 citations

We investigate low-energy excitations of the one-dimensional half-filled SU(4) Hubbard model with an attractive on-site interaction

U<0

U

, while the spin gap and others increase with increasing

\ensuremath{\mid}U\ensuremath{\mid}

and have linear asymptotic behaviors.

We study a one-dimensional SU(N) Hubbard model with an attractive on-site interaction and

N>2

at half-filling on the bipartite lattice using density-matrix renormalization-group method and a perturbation theory. We find that the ground state of the SU(N) Hubbard model is a charge density wave state with two-fold degeneracy. All the excitations are found to be gapful, resulting in an insulating ground state, on contrary to that in the SU(2) case. Moreover, the charge gap is equal to the Cooperon gap, which behaves as

-2Nt^2/(N-1)U

in the strong coupling regime. However, the spin gap

Δ_{s}

and the quasiparticle gap

Δ_{1}

as well open exponentially in the weak coupling region, while in the strong coupling region, they linearly depend on

U

such that

Δ_{s}\sim -U(N-1)

and

Δ_{1}\sim -U(N-1)/2

The one-dimensional

\mathrm{SU}(n)

Hubbard model is investigated numerically for

n=2

, 3, 4, and 5 at half-filling and

1∕n

filling using the density-matrix renormalization-group method. The energy gaps and various quantum information entropies are calculated. In the half-filled case, finite spin and charge gaps are found for arbitrary positive

U

n>2

. Furthermore, it is shown that the transition to the gapped phase at

{U}_{c}=0

is of Kosterlitz-Thouless type and is accompanied by a bond dimerization both for even and odd

n

. In the

1∕n

-filled case, the transition has similar features as the metal-insulator transition in the half-filled SU(2) Hubbard model. The charge gap opens exponentially slowly for

U>{U}_{c}=0

, the spin sector remains gapless, and the ground state is nondimerized.

U_{a}\\not=U_{b}

U_{a}>0

U_{b}>0

. The ground-state phase diagram is obtained in the limit of second order renormalization. Depending on the sign and relative values of the bare coupling constants, there is a gap in the spin or charge excitation spectrum and the model system tends to superconducting or antiferromagnetic order at T=0, with doubled period. The role of interaction between particles on nearest and next-nearest neighbor sites is also considered.