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:1403.4315 · Physical Review B

Spin density waves in the Hubbard model: A DMFT approach

Robert Peters, Norio Kawakami

Published Apr 24, 2014• 46 citations
arXivHTMLPDF

Abstract

We analyze spin density waves (SDWs) in the Hubbard model on a square lattice within the framework of inhomogeneous dynamical mean field theory (IDMFT). Doping the half-filled Hubbard model results in a change of the antiferromagnetic N\'eel state, which exists exactly at half filling, to a phase of incommensurate SDWs. Previous studies of this phase mainly rely on static mean field calculations. In this paper, we will use large-scale IDMFT calculations to study properties of SDWs in the Hubbard model. A great advantage of IDMFT over static mean field approaches is the inclusion of local screening effects and the easy access to dynamical correlation functions. Furthermore, this technique is not restricted to the Hubbard model, but can be easily used to study incommensurate phases in various strongly correlated materials.

DOI
10.1103/physrevb.89.155134

Related papers

Soliton Lattice Modulation of Incommensurate Spin Density Wave in Two Dimensional Hubbard Model -A Mean Field Study-

Masaru Kato, Kazushige Machida, Hiizu Nakanishi +1 more

Spatially modulated magnetic phases are investigated within the mean field theory for an itinerant electron model, i.e. the Hubbard model on a two-dimensional square lattice. By numerically diagonalizing the Hamiltonian for finite-size systems under a periodic boundary condition, we examine relative stability and physical properties of several possible magnetic states. When the electron fillings are nearly half-full, the diagonally or vertically modulated spin density wave (SDW) state is stabilized over the uniform antiferromagnetic state and a crossover from the vertical to the diagonal states appears. The diagonal or vertical stripe state is characterized by the presence of the midgap band due to the soliton lattice formation inside the main SDW gap, being an insulator. The wave length λ SDW is linearly proportional to the excess carrier concentration. Excess carriers are accommodated in the form of the soliton lattice, forming a charge density wave whose wave length is λ SDW /2.

Journal of the Physical Society of Japan•Mar 15, 1990•285 citations

Theory of the extended Hubbard model at half filling

Xin-Zhong Yan

The square-lattice extended Hubbard model at half filling is studied by a perturbation scheme. By taking into account the ground state of the mean-field theory as a reference state, the scheme treats the collective fluctuations beyond the mean field as the predominant perturbation. The system at ground state can be a spin-density wave (SDW) or a charge-density wave (CDW) depending on the relative strengths of the on-site electron interaction and the nearest-neighbor interaction. The excitation modes above the ground state are analyzed through diagonalizing an effective Hamiltonian. The energy spectra and the wave functions are self-consistently given by the formalism. By comparing the ground-state energies, we investigate the SDW-CDW transition.

Physical review. B, Condensed matter•Sep 1, 1993•32 citations

The two orbital Hubbard model in a square lattice: a DMFT + DMRG approach

Y. Núñez-Fernández, Daniel J. García, K. Hallberg

We develop a precise and reliable numerical method for the calculation of electronic properties of the two orbital Hubbard model in a square lattice at half filling, based on the Dynamical Mean Field Theory (DMFT). We use the Density Matrix Renormalization Group (DMRG) as the impurity solver for the DMFT's selfconsistent equations to obtain accurate values for the Green's functions on the real axis. This way, reliable densities of states are obtained that do not need to resort to analytical continuation methods as those using quantum Monte Carlo techniques. Large system sizes can be achieved with increasing accuracy.

Journal of Physics Conference Series•Dec 8, 2014•3 citations

Dynamically enhanced magnetic incommensurability: Effects of local dynamics on nonlocal spin correlations in a strongly correlated metal

Demetrio Vilardi, Ciro Taranto, Walter Metzner

We compute the spin susceptibility of the two-dimensional Hubbard model away from half-filling, and analyze the impact of frequency-dependent vertex corrections as obtained from the dynamical mean field theory (DMFT). We find that the local dynamics captured by the DMFT vertex strongly affects nonlocal spin correlations, and thus the momentum dependence of the spin susceptibility. While the widely used random-phase approximation yields commensurate N\'eel-type antiferromagnetism as the dominant instability over a wide doping range, the vertex corrections favor incommensurate ordering wave vectors away from $(\ensuremath{\pi},\ensuremath{\pi})$. Our results indicate that the connection between the magnetic ordering wave vector and the Fermi surface geometry, familiar for weakly interacting systems, can hold in a strongly correlated metal, too.

arXiv:1803.06175•Physical review. B./Physical review. B•Jun 7, 2018•16 citations

Incommensurate spiral magnetic order on anisotropic triangular lattice: Dynamical mean-field study in a spin-rotating frame

Shimpei Goto, Susumu Kurihara, Daisuke Yamamoto

We study the ground-state magnetism of the half-filled Hubbard model on the anisotropic triangular lattice, where two out of three bonds have hopping $t$ and the third one has ${t}^{\ensuremath{'}}$ in a unit triangle. Working in a spin-rotating frame and using the density matrix renormalization group method as an impurity solver, we provide a proper description of incommensurate magnetizations at zero temperature in the framework of the dynamical mean-field theory (DMFT). It is shown that the incommensurate spiral magnetic order for ${t}^{\ensuremath{'}}/t\ensuremath{\gtrsim}0.7$ survives the dynamical fluctuations of itinerant electrons in the Hubbard interaction range from the strong-coupling (localized-spin) limit down to the insulator-to-metal transition. We also find that when the anisotropy parameter ${t}^{\ensuremath{'}}/t$ increases from the N\'eel-to-spiral transition, the magnitude of the magnetic moment exhibits a maximum at the isotropic triangular lattice point ${t}^{\ensuremath{'}}/t=1$ and then rapidly decreases in the range of larger ${t}^{\ensuremath{'}}/t$. This work gives a solid foundation for further extension of the study including nonlocal correlation effects neglected at the standard DMFT level.

arXiv:1608.04490•Physical review. B./Physical review. B•Dec 28, 2016•17 citations

Doping dependence of the internal energy, spin-density-wave order parameter, and the chemical potential for the Hubbard model

Hongguang Chi, A. D. S. Nagi

We have applied mean-field theory to calculate the spin-density-wave (SDW) order parameter \ensuremath{\Delta}, the chemical potential \ensuremath{\mu}, and the ground-state energy at various band fillings for the Hubbard model. We have found that at zero temperature and in the large-U limit, the SDW order parameter and the ground-state energy can be written as \ensuremath{\Delta}=U(1-x)/2-O(J) and ${\mathit{E}}_{\mathit{g}}$=-U(1-x${)}^{2}$/4-0(J). The chemical potential obtained here for x=0 and 1 agrees well with the result obtained by the exact-diagonalization calculation on a 4\ifmmode\times\else\texttimes\fi{}4 sites cluster by Dagotto et al. [Phys. Rev. B 45, 10 741 (1992)]. In the SDW phase, the mean-field theory gives an upward shift in the chemical potential as one dopes away from half-filling, which is in contrast with the exact-diagonalization calculations. This result indicates that the Mott-Hubbard gap is depressed much more rapidly in the mean-field theory than the exact-diagonalization calculation. The doping dependence of ground-state energy calculated here is in good agreement with the above numerical calculation for doping up to 0.5. Here, U is the intrasite Coulomb repulsion, x is doping concentration, J=4${\mathit{t}}^{2}$/U is the superexchange interaction parameter, and t is the hopping integral for the nearest neighbors.

Physical review. B, Condensed matter•May 1, 1994•1 citation
We analyze spin density waves (SDWs) in the Hubbard model on a square lattice within the framework of inhomogeneous dynamical mean field theory (IDMFT). Doping the half-filled Hubbard model results in a change of the antiferromagnetic N'eel state, which exists exactly at half filling, to a phase of incommensurate SDWs. Previous studies of this phase mainly rely on static mean field calculations. In this paper, we will use large-scale IDMFT calculations to study properties of SDWs in the Hubbard model. A great advantage of IDMFT over static mean field approaches is the inclusion of local screening effects and the easy access to dynamical correlation functions. Furthermore, this technique is not restricted to the Hubbard model, but can be easily used to study incommensurate phases in various strongly correlated materials.
Spatially modulated magnetic phases are investigated within the mean field theory for an itinerant electron model, i.e. the Hubbard model on a two-dimensional square lattice. By numerically diagonalizing the Hamiltonian for finite-size systems under a periodic boundary condition, we examine relative stability and physical properties of several possible magnetic states. When the electron fillings are nearly half-full, the diagonally or vertically modulated spin density wave (SDW) state is stabilized over the uniform antiferromagnetic state and a crossover from the vertical to the diagonal states appears. The diagonal or vertical stripe state is characterized by the presence of the midgap band due to the soliton lattice formation inside the main SDW gap, being an insulator. The wave length λ SDW is linearly proportional to the excess carrier concentration. Excess carriers are accommodated in the form of the soliton lattice, forming a charge density wave whose wave length is λ SDW /2.
The square-lattice extended Hubbard model at half filling is studied by a perturbation scheme. By taking into account the ground state of the mean-field theory as a reference state, the scheme treats the collective fluctuations beyond the mean field as the predominant perturbation. The system at ground state can be a spin-density wave (SDW) or a charge-density wave (CDW) depending on the relative strengths of the on-site electron interaction and the nearest-neighbor interaction. The excitation modes above the ground state are analyzed through diagonalizing an effective Hamiltonian. The energy spectra and the wave functions are self-consistently given by the formalism. By comparing the ground-state energies, we investigate the SDW-CDW transition.
We develop a precise and reliable numerical method for the calculation of electronic properties of the two orbital Hubbard model in a square lattice at half filling, based on the Dynamical Mean Field Theory (DMFT). We use the Density Matrix Renormalization Group (DMRG) as the impurity solver for the DMFT's selfconsistent equations to obtain accurate values for the Green's functions on the real axis. This way, reliable densities of states are obtained that do not need to resort to analytical continuation methods as those using quantum Monte Carlo techniques. Large system sizes can be achieved with increasing accuracy.
We compute the spin susceptibility of the two-dimensional Hubbard model away from half-filling, and analyze the impact of frequency-dependent vertex corrections as obtained from the dynamical mean field theory (DMFT). We find that the local dynamics captured by the DMFT vertex strongly affects nonlocal spin correlations, and thus the momentum dependence of the spin susceptibility. While the widely used random-phase approximation yields commensurate N\'eel-type antiferromagnetism as the dominant instability over a wide doping range, the vertex corrections favor incommensurate ordering wave vectors away from $(\ensuremath{\pi},\ensuremath{\pi})$. Our results indicate that the connection between the magnetic ordering wave vector and the Fermi surface geometry, familiar for weakly interacting systems, can hold in a strongly correlated metal, too.
We study the ground-state magnetism of the half-filled Hubbard model on the anisotropic triangular lattice, where two out of three bonds have hopping ttt and the third one has ${t}^{\ensuremath{'}}$ in a unit triangle. Working in a spin-rotating frame and using the density matrix renormalization group method as an impurity solver, we provide a proper description of incommensurate magnetizations at zero temperature in the framework of the dynamical mean-field theory (DMFT). It is shown that the incommensurate spiral magnetic order for ${t}^{\ensuremath{'}}/t\ensuremath{\gtrsim}0.7$ survives the dynamical fluctuations of itinerant electrons in the Hubbard interaction range from the strong-coupling (localized-spin) limit down to the insulator-to-metal transition. We also find that when the anisotropy parameter ${t}^{\ensuremath{'}}/t$ increases from the N\'eel-to-spiral transition, the magnitude of the magnetic moment exhibits a maximum at the isotropic triangular lattice point ${t}^{\ensuremath{'}}/t=1$ and then rapidly decreases in the range of larger ${t}^{\ensuremath{'}}/t$. This work gives a solid foundation for further extension of the study including nonlocal correlation effects neglected at the standard DMFT level.
We have applied mean-field theory to calculate the spin-density-wave (SDW) order parameter \ensuremath{\Delta}, the chemical potential \ensuremath{\mu}, and the ground-state energy at various band fillings for the Hubbard model. We have found that at zero temperature and in the large-U limit, the SDW order parameter and the ground-state energy can be written as \ensuremath{\Delta}=U(1-x)/2-O(J) and Eg{\mathit{E}}_{\mathit{g}}Eg​=-U(1-x)2{)}^{2})2/4-0(J). The chemical potential obtained here for x=0 and 1 agrees well with the result obtained by the exact-diagonalization calculation on a 4\ifmmode\times\else\texttimes\fi{}4 sites cluster by Dagotto et al. [Phys. Rev. B 45, 10 741 (1992)]. In the SDW phase, the mean-field theory gives an upward shift in the chemical potential as one dopes away from half-filling, which is in contrast with the exact-diagonalization calculations. This result indicates that the Mott-Hubbard gap is depressed much more rapidly in the mean-field theory than the exact-diagonalization calculation. The doping dependence of ground-state energy calculated here is in good agreement with the above numerical calculation for doping up to 0.5. Here, U is the intrasite Coulomb repulsion, x is doping concentration, J=4t2{\mathit{t}}^{2}t2/U is the superexchange interaction parameter, and t is the hopping integral for the nearest neighbors.