Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:cond-mat/9510106 · Physical review. B, Condensed matter

Numerical renormalization-group study of the one-dimensionalt-Jmodel

Liang Chen, S. Moukouri

Published Jan 15, 1996• 12 citations
arXivHTMLPDF

Abstract

The one-dimensional t-J model is investigated using the density-matrix renormalization-group (DMRG) method. We report a generalization of the DMRG method to the case of arbitrary band filling and prove a theorem with respect to the reduced density matrix that accelerates the numerical computation. Lastly, using the extended DMRG method, we present the ground-state electron momentum distribution, as well as spin- and charge-correlation functions. The 3${\mathit{k}}_{\mathit{F}}$ anomaly of the momentum distribution function discussed by Ogata and Shiba is shown to disappear as J increases. We also argue that there exists a density-independent ${\mathit{J}}_{\mathit{c}}$ beyond which the system becomes an electron solid. \textcopyright{} 1996 The American Physical Society.

DOI
10.1103/physrevb.53.1866

Related papers

The one-dimensional Kondo lattice model studied by the density matrix renormalization group method

Naokazu Shibata, Kazuo Ueda

Recent developments in the theoretical investigation of the one-dimensional Kondo lattice model by using the density matrix renormalization group (DMRG) method are discussed in this review. Short summaries are given of the zero-temperature DMRG method, the finite-temperature DMRG method, and also the application of the finite- T DMRG to dynamic quantities. Away from half-filling, the paramagnetic metallic state is shown to be a Tomonaga-Luttinger liquid with a large Fermi surface. The size of the large Fermi surface is determined by the sum of the densities of the conduction electrons and the localized spins. The correlation exponent of this metallic phase is smaller than 1/2. At half-filling the ground state is insulating. The excitation gaps are different, depending on the channels, the spin gap, the charge gap and the quasiparticle gap. The temperature dependence of the spin and charge susceptibilities and the specific heat are discussed. Particularly interesting is the temperature dependence of various excitation spectra, which indicates unusual properties for the Kondo insulators.

arXiv:cond-mat/9808301•Journal of Physics Condensed Matter•Jan 1, 1999•71 citations

Density-matrix renormalization-group calculation of correlation functions in the one-dimensional Hubbard model

Shaojin Qin, Shoudan Liang, Zhao-Bin Su +1 more

We have studied correlation functions of the one-dimensional Hubbard model using the density-matrix numerical renormalization-group approach. The singularity exponents of the momentum distribution at k=${\mathit{k}}_{\mathit{F}}$ and 3${\mathit{k}}_{\mathit{F}}$, as well as the power-law singularity of the spin-correlation function, are computed for large U (U/t=${10}^{3}$). The momentum-distribution exponent at k=${\mathit{k}}_{\mathit{F}}$ and the spin-correlation exponent are in agreement with the analytic results, while the calculated exponent for momentum distribution at k=3${\mathit{k}}_{\mathit{F}}$ is about 3/4, which disagrees with the analytically predicted value 9/8. We also discuss several techniques for an accurate calculation of the correlation functions.

Physical review. B, Condensed matter•Aug 15, 1995•30 citations

Correlation functions in the one-dimensionalt-Jmodel

Norio Kawakami, Sung-Kil Yang

The critical exponents for the charge, spin, electron, and superconducting correlation functions of the one-dimensional t-J model at t=J are obtained for arbitrary band filling. Our method is based on the Bethe-ansatz solution and the finite-size scaling analysis in conformal field theory. The long-distance behavior of the model belongs to the same universality class as the repulsive Hubbard model. Near half-filling the exponents take the values expected in the strong-correlation limit of the Hubbard model. In the low-density limit the exponents are those of the noninteracting system.

Physical Review Letters•Oct 29, 1990•169 citations

Hybrid-space density matrix renormalization group study of the doped two-dimensional Hubbard model

G. Ehlers, Steven R. White, R. M. Noack

The performance of the density matrix renormalization group (DMRG) is strongly influenced by the choice of the local basis of the underlying physical lattice. We demonstrate that, for the two-dimensional Hubbard model, the hybrid--real-momentum-space formulation of the DMRG is computationally more efficient than the standard real-space formulation. In particular, we show that the computational cost for fixed bond dimension of the hybrid-space DMRG is approximately independent of the width of the lattice, in contrast to the real-space DMRG, for which it is proportional to the width squared. We apply the hybrid-space algorithm to calculate the ground state of the doped two-dimensional Hubbard model on cylinders of width four and six sites; at $n=0.875$ filling, the ground state exhibits a striped charge-density distribution with a wavelength of eight sites for both $U/t=4.0$ and $8.0$. We find that the strength of the charge ordering depends on $U/t$ and on the boundary conditions. Furthermore, we investigate the magnetic ordering as well as the decay of the static spin, charge, and pair-field correlation functions.

arXiv:1701.03690•Physical review. B./Physical review. B•Mar 21, 2017•90 citations

Ground-state properties of the one-dimensional Kondo lattice at partial band filling

S. Moukouri, Laurent G. Caron

We compute the magnetic structure factor, the singlet correlation function, and the momentum distribution of the one-dimensional Kondo lattice model at the density \ensuremath{\rho}=0.7. The density-matrix--renormalization-group method is used. We show that in the weak-coupling regime, the ground state is paramagnetic. We argue that a Luttinger-liquid description of the model in this region is consistent with our calculations. In the strong-coupling regime, the ground state becomes ferromagnetic. The conduction electrons show a spinless-fermionlik

arXiv:cond-mat/9510087•Physical review. B, Condensed matter•Dec 1, 1995•46 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.

arXiv:cond-mat/0110420•Physical review. B, Condensed matter•Apr 10, 2002•37 citations
The one-dimensional t-J model is investigated using the density-matrix renormalization-group (DMRG) method. We report a generalization of the DMRG method to the case of arbitrary band filling and prove a theorem with respect to the reduced density matrix that accelerates the numerical computation. Lastly, using the extended DMRG method, we present the ground-state electron momentum distribution, as well as spin- and charge-correlation functions. The 3kF{\mathit{k}}_{\mathit{F}}kF​ anomaly of the momentum distribution function discussed by Ogata and Shiba is shown to disappear as J increases. We also argue that there exists a density-independent Jc{\mathit{J}}_{\mathit{c}}Jc​ beyond which the system becomes an electron solid. \textcopyright{} 1996 The American Physical Society.
Recent developments in the theoretical investigation of the one-dimensional Kondo lattice model by using the density matrix renormalization group (DMRG) method are discussed in this review. Short summaries are given of the zero-temperature DMRG method, the finite-temperature DMRG method, and also the application of the finite- T DMRG to dynamic quantities. Away from half-filling, the paramagnetic metallic state is shown to be a Tomonaga-Luttinger liquid with a large Fermi surface. The size of the large Fermi surface is determined by the sum of the densities of the conduction electrons and the localized spins. The correlation exponent of this metallic phase is smaller than 1/2. At half-filling the ground state is insulating. The excitation gaps are different, depending on the channels, the spin gap, the charge gap and the quasiparticle gap. The temperature dependence of the spin and charge susceptibilities and the specific heat are discussed. Particularly interesting is the temperature dependence of various excitation spectra, which indicates unusual properties for the Kondo insulators.
We have studied correlation functions of the one-dimensional Hubbard model using the density-matrix numerical renormalization-group approach. The singularity exponents of the momentum distribution at k=kF{\mathit{k}}_{\mathit{F}}kF​ and 3kF{\mathit{k}}_{\mathit{F}}kF​, as well as the power-law singularity of the spin-correlation function, are computed for large U (U/t=103{10}^{3}103). The momentum-distribution exponent at k=kF{\mathit{k}}_{\mathit{F}}kF​ and the spin-correlation exponent are in agreement with the analytic results, while the calculated exponent for momentum distribution at k=3kF{\mathit{k}}_{\mathit{F}}kF​ is about 3/4, which disagrees with the analytically predicted value 9/8. We also discuss several techniques for an accurate calculation of the correlation functions.
The critical exponents for the charge, spin, electron, and superconducting correlation functions of the one-dimensional t-J model at t=J are obtained for arbitrary band filling. Our method is based on the Bethe-ansatz solution and the finite-size scaling analysis in conformal field theory. The long-distance behavior of the model belongs to the same universality class as the repulsive Hubbard model. Near half-filling the exponents take the values expected in the strong-correlation limit of the Hubbard model. In the low-density limit the exponents are those of the noninteracting system.
The performance of the density matrix renormalization group (DMRG) is strongly influenced by the choice of the local basis of the underlying physical lattice. We demonstrate that, for the two-dimensional Hubbard model, the hybrid--real-momentum-space formulation of the DMRG is computationally more efficient than the standard real-space formulation. In particular, we show that the computational cost for fixed bond dimension of the hybrid-space DMRG is approximately independent of the width of the lattice, in contrast to the real-space DMRG, for which it is proportional to the width squared. We apply the hybrid-space algorithm to calculate the ground state of the doped two-dimensional Hubbard model on cylinders of width four and six sites; at n=0.875n=0.875n=0.875 filling, the ground state exhibits a striped charge-density distribution with a wavelength of eight sites for both U/t=4.0U/t=4.0U/t=4.0 and 8.08.08.0. We find that the strength of the charge ordering depends on U/tU/tU/t and on the boundary conditions. Furthermore, we investigate the magnetic ordering as well as the decay of the static spin, charge, and pair-field correlation functions.
We compute the magnetic structure factor, the singlet correlation function, and the momentum distribution of the one-dimensional Kondo lattice model at the density \ensuremath{\rho}=0.7. The density-matrix--renormalization-group method is used. We show that in the weak-coupling regime, the ground state is paramagnetic. We argue that a Luttinger-liquid description of the model in this region is consistent with our calculations. In the strong-coupling regime, the ground state becomes ferromagnetic. The conduction electrons show a spinless-fermionlik
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/r1/r1/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.