arXiv:cond-mat/0503731 · Physical Review B

Correlation effects for semiconducting single-wall carbon nanotubes: A density matrix renormalization group study

Fei Ye, Bing-Shen Wang, Jizhong Lou, Zhao-Bin Su

Published Dec 30, 2005• 6 citations

Abstract

In this paper we report the applicability of the density matrix renormalization group (DMRG) approach to the cylindrical single wall carbon nanotube (SWCN) for the purpose of its correlation effect. By applying the DMRG approach to the $t+U+V$ model, with $t$ and $V$ being the hopping and Coulomb energies between the nearest neighboring sites, respectively, and $U$ the on-site Coulomb energy, we calculate the phase diagram for the SWCN with chiral numbers (${n}_{1}=3$, ${n}_{2}=2$), which reflects the competition between the correlation energy $U$ and $V$. Within reasonable parameter ranges, we investigate possible correlated ground states, the lowest excitations, and the corresponding correlation functions in which the connection with the excitonic insulator is particularly addressed.

DOI: 10.1103/physrevb.72.233409

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arXiv:cond-mat/0503731 · Physical Review B

Correlation effects for semiconducting single-wall carbon nanotubes: A density matrix renormalization group study

Fei Ye, Bing-Shen Wang, Jizhong Lou, Zhao-Bin Su

Published Dec 30, 2005• 6 citations

arXiv HTML PDF

Abstract

t+U+V

model, with

t

and

V

being the hopping and Coulomb energies between the nearest neighboring sites, respectively, and

U

the on-site Coulomb energy, we calculate the phase diagram for the SWCN with chiral numbers (

{n}_{1}=3

{n}_{2}=2

), which reflects the competition between the correlation energy

U

and

V

. Within reasonable parameter ranges, we investigate possible correlated ground states, the lowest excitations, and the corresponding correlation functions in which the connection with the excitonic insulator is particularly addressed.

DOI: 10.1103/physrevb.72.233409

Related papers

Correlation effects for chiral semiconducting single wall carbon nanotube: a density matrix renormalization group study

Fei Ye, Bing-Shen Wang, Jizhong Lou +1 more

Mar 31, 20050 citations

Application of the density matrix renormalization group in momentum space

Satoshi Nishimoto, Eric Jeckelmann, Florian Gebhard +1 more

We investigate the application of the density matrix renormalization group (DMRG) to the Hubbard model in momentum space. We treat the one-dimensional models with dispersion relations corresponding to nearest-neighbor hopping and $1/r$ hopping and the two-dimensional model with isotropic nearest-neighbor hopping. By comparing with the exact solutions for both one-dimensional models and with exact diagonalization in two dimensions, we first investigate the convergence of the ground-state energy. We find variational convergence of the energy with the number of states kept for all models and parameter sets. In contrast to the real-space algorithm, the accuracy becomes rapidly worse with increasing interaction and is not significantly better at half filling. We compare the results for different dispersion relations at fixed interaction strength over bandwidth and find that extending the range of the hopping in one dimension has little effect, but that changing the dimensionality from one to two leads to lower accuracy at weak-to-moderate interaction strength. In the one-dimensional models at half filling, we also investigate the behavior of the single-particle gap, the dispersion of spinon excitations, and the momentum distribution function. For the single-particle gap, we find that proper extrapolation in the number of states kept is important. For the spinon dispersion, we find that good agreement with the exact forms can be achieved at weak coupling if the large momentum-dependent finite-size effects are taken into account for nearest-neighbor hopping. For the momentum distribution, we compare with various weak-coupling and strong-coupling approximations and discuss the importance of finite-size effects as well as the accuracy of the DMRG.We investigate the application of the density matrix renormalization group (DMRG) to the Hubbard model in momentum space. We treat the one-dimensional models with dispersion relations corresponding to nearest-neighbor hopping and $1/r$ hopping and the two-dimensional model with isotropic nearest-neighbor hopping. By comparing with the exact solutions for both one-dimensional models and with exact diagonalization in two dimensions, we first investigate the convergence of the ground-state energy. We find variational convergence of the energy with the number of states kept for all models and parameter sets. In contrast to the real-space algorithm, the accuracy becomes rapidly worse with increasing interaction and is not significantly better at half filling. We compare the results for different dispersion relations at fixed interaction strength over bandwidth and find that extending the range of the hopping in one dimension has little effect, but that changing the dimensionality from one to two leads to lower accuracy at weak-to-moderate interaction strength. In the one-dimensional models at half filling, we also investigate the behavior of the single-particle gap, the dispersion of spinon excitations, and the momentum distribution function. For the single-particle gap, we find that proper extrapolation in the number of states kept is important. For the spinon dispersion, we find that good agreement with the exact forms can be achieved at weak coupling if the large momentum-dependent finite-size effects are taken into account for nearest-neighbor hopping. For the momentum distribution, we compare with various weak-coupling and strong-coupling approximations and discuss the importance of finite-size effects as well as the accuracy of the DMRG.

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A DMRG study of the half-filled Hubbard model on a Bethe lattice: a signature of the Mott-Hubbard transition

Marie-Bernadette Lepetit, Maixent Cousy

The half-filled Hubbard model on the Bethe lattice with coordination number $z=3$ is studied using the density-matrix renormalization group (DMRG) method. Ground-state properties such as the energy $E$ , average local magnetization $ $, its fluctuations $ - ^2$ and various spin correlation functions $ - $ are determined as a function of the Coulomb interaction strength $U/t$ . The calculated local magnetic moments $ $ increase monotonically with increasing Coulomb repulsion $U/t$ forming an antiferromagnetic spin-density-wave state which matches the two sublattices of the bipartite Bethe lattice. At large $U/t$ , $ $ is strongly reduced with respect to the saturation value 1/2 due to exchange fluctuations between nearest neighbors (NN) spins ( $| |\simeq 0.35$ for $U/t\to +\infty$ ). $ - ^2$ shows a maximum for $U/t=2.4$ --2.9 which results from the interplay between the usual increase of $ $ with increasing $U/t$ and the formation of important permanent moments $ $ at large $U/t$ . NN sites show antiferromagnetic spin correlations which increase with increasing Coulomb repulsion. In contrast next NN sites are very weakly correlated over the whole range of $U/t$ . The accuracy of the DMRG results is discussed by comparison with tight-binding exact results, independent DMRG calculations for the Heisenberg model and simple first-order perturbation estimates.The half-filled Hubbard model on the Bethe lattice with coordination number $z=3$ is studied using the density-matrix renormalization group (DMRG) method. Ground-state properties such as the energy $E$, average local magnetization $ $, its fluctuations $ - ^2$ and various spin correlation functions $ - $ are determined as a function of the Coulomb interaction strength $U/t$. The calculated local magnetic moments $ $ increase monotonically with increasing Coulomb repulsion $U/t$ forming an antiferromagnetic spin-density-wave state which matches the two sublattices of the bipartite Bethe lattice. At large $U/t$, $ $ is strongly reduced with respect to the saturation value 1/2 due to exchange fluctuations between nearest neighbors (NN) spins ($| |\simeq 0.35$ for $U/t\to +\infty$). $ - ^2$ shows a maximum for $U/t=2.4$--2.9 which results from the interplay between the usual increase of $ $ with increasing $U/t$ and the formation of important permanent moments $ $ at large $U/t$. NN sites show antiferromagnetic spin correlations which increase with increasing Coulomb repulsion. In contrast next NN sites are very weakly correlated over the whole range of $U/t$. The accuracy of the DMRG results is discussed by comparison with tight-binding exact results, independent DMRG calculations for the Heisenberg model and simple first-order perturbation estimates.

Jan 22, 19980 citations

t+U+V

model, with

t

and

V

being the hopping and Coulomb energies between the nearest neighboring sites, respectively, and

U

the on-site Coulomb energy, we calculate the phase diagram for the SWCN with chiral numbers (

{n}_{1}=3

{n}_{2}=2

), which reflects the competition between the correlation energy

U

and

V

1/r

hopping and the two-dimensional model with isotropic nearest-neighbor hopping. By comparing with the exact solutions for both one-dimensional models and with exact diagonalization in two dimensions, we first investigate the convergence of the ground-state energy. We find variational convergence of the energy with the number of states kept for all models and parameter sets. In contrast to the real-space algorithm, the accuracy becomes rapidly worse with increasing interaction and is not significantly better at half filling. We compare the results for different dispersion relations at fixed interaction strength over bandwidth and find that extending the range of the hopping in one dimension has little effect, but that changing the dimensionality from one to two leads to lower accuracy at weak-to-moderate interaction strength. In the one-dimensional models at half filling, we also investigate the behavior of the single-particle gap, the dispersion of spinon excitations, and the momentum distribution function. For the single-particle gap, we find that proper extrapolation in the number of states kept is important. For the spinon dispersion, we find that good agreement with the exact forms can be achieved at weak coupling if the large momentum-dependent finite-size effects are taken into account for nearest-neighbor hopping. For the momentum distribution, we compare with various weak-coupling and strong-coupling approximations and discuss the importance of finite-size effects as well as the accuracy of the DMRG.

d

-wave Mott insulator, an

s

-wave Mott insulator, a

p

-density wave, and a charge density wave. The doped case has two ground-state phases, a

d

-wave superconductor and a phase where a

p

density wave and a charge density wave coexist. We also explore the global phase diagram with a general interaction profile and find several additional states, including a chiral current phase where current flows around the nanotube along the zigzag bonds.

The half-filled Hubbard model on the Bethe lattice with coordination number

z=3

is studied using the density-matrix renormalization group (DMRG) method. Ground-state properties such as the energy

E

, average local magnetization $ $, its fluctuations $ - ^2$ and various spin correlation functions $ - $ are determined as a function of the Coulomb interaction strength

U/t

. The calculated local magnetic moments $ $ increase monotonically with increasing Coulomb repulsion

U/t

forming an antiferromagnetic spin-density-wave state which matches the two sublattices of the bipartite Bethe lattice. At large

U/t

, $ $ is strongly reduced with respect to the saturation value 1/2 due to exchange fluctuations between nearest neighbors (NN) spins (

| |\simeq 0.35

for

U/t\to +\infty

). $ - ^2$ shows a maximum for

U/t=2.4

--2.9 which results from the interplay between the usual increase of $ $ with increasing

U/t

and the formation of important permanent moments $ $ at large

U/t

. NN sites show antiferromagnetic spin correlations which increase with increasing Coulomb repulsion. In contrast next NN sites are very weakly correlated over the whole range of

U/t

. The accuracy of the DMRG results is discussed by comparison with tight-binding exact results, independent DMRG calculations for the Heisenberg model and simple first-order perturbation estimates.