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

Physical review. B, Condensed matter

Collective excitations and sum rules for the Hubbard model in the spin-density-wave regime

H. Monien, Kevin S. Bedell

Published Feb 1, 1992• 17 citations
Publisher

Abstract

A variational estimate for the spin-wave velocity of the one-band Hubbard model on a square lattice in the spin-density-wave regime is studied. The estimate is given by the ratio of the f-sum rule to the static structure factor of the transverse-spin response function. The known results for the Heisenberg model are used to obtain results for those quantities in the large-U limit of the Hubbard model. The f-sum rule and static structure factor are calculated using the random-phase approximation (RPA). The spin-wave velocity calculated in the RPA, in the spin-density wave ground state, violates the variational bound.

DOI
10.1103/physrevb.45.3164

Related papers

Spin Waves in the Half-Filled Hubbard Model beyond the Random Phase Approximation

P. J. H. Denteneer, J. M. J. van Leeuwen

The velocity of long-wavelength spin waves for the two-dimensional Hubbard model on a square lattice at half-filling is calculated using the variational Monte Carlo method with a Gutzwiller-type wave function. We show that the result from the Random Phase Approximation (RPA) for the spin wave velocity can also be found as the square root of the ratio of the helicity modulus and the perpendicular susceptibility as calculated in the Hartree-Fock approximation (HFA). Since the Gutzwiller wave function improves upon the HFA, our result for the spin wave velocity improves upon the RPA result. For the on-site repulsion U between 3 and 12 times the hopping integral t the spin wave velocity increases by 34 to 15% compared to the RPA result.

Europhysics Letters (EPL)•May 20, 1993•9 citations

Variational calculations for the square-lattice quantum antiferromagnet

Zhiping Liu, Efstratios Manousakis

We study the spin-1/2 Heisenberg antiferromagnet on a square lattice using variational Monte Carlo calculations. We construct a variational wave function which gives accurate ground-state energy and is consistent with sum rules for the dynamical structure function. The spin-wave velocity and the spin-stiffness constant can be calculated using sum rules. We obtain ${Z}_{c}$==c/${c}_{0}$, where ${c}_{0}$ is the classical spin-wave velocity. This and other ground-state quantities are in good agreement with spin-wave theory and Monte Carlo calculations.

Physical review. B, Condensed matter•Dec 1, 1989•35 citations

The Spin Stiffness and the Transverse Susceptibility of the Half-Filled Hubbard Model

Zhu-Pei Shi, Rajiv R. P. Singh

The T = 0 spin stiffness ρ s and the transverse susceptibility χ ⊥ of the square lattice half-filled Hubbard model are calculated as a function of the Hubbard parameter ratio U / t by series expansions around the Ising limit. We find that the calculated spin stiffness, transverse susceptibility, and sublattice magnetization for the Hubbard model smoothly approach the Heisenberg values for large U / t . The results are compared for different U / t with RPA and other numerical studies. The uniform susceptibility data indicate a crossover around U / t ≈ 4 between weak-coupling (spin density wave) behavior at small U and strong-coupling (Heisenberg) behavior at large U .

arXiv:cond-mat/9508005•Europhysics Letters (EPL)•Aug 1, 1995•8 citations

Collective Modes of Incommensurate Spin Density Wave in One-Dimensional Hubbard Model

Masanori Ichioka, Eiji Kaneshita, Kazushige Machida

Dynamical spin and charge susceptibility and collective modes are studied in the framework of the random phase approximation. They are calculated from the wave function of the selfconsistently obtained ground state, including all possible higher harmonics components of the ordering vector Q . We investigate a spin wave excitation in the spin transverse mode, and phason excitation related to the domain-wall motion in the spin longitudinal and charge modes. We consider the dispersion curve of the collective mode, and discuss the dependence on the on-site U interaction and the period of the incommensurate structure.

Journal of the Physical Society of Japan•Mar 15, 2001•12 citations

Spectral properties of the large-negative-U Hubbard model

Henk J. Eskes, Andrzej M. Oleś

Using the formalism introduced by Harris and Lange [Phys. Rev. 157, 295 (1967)] explicit expressions for partial sum rules of the individual Hubbard bands in the large-negative-U limit are derived. The one-particle spectrum, optical spectrum, as well as charge- and spin-response functions are considered. The approach gives a transparent description of the main features of these spectra. The main sum rules depend on only two independent nearest-neighbor expectation values which are estimated in the ground state using numerical calculations, exact results, and linear-spin-wave theory. Simple expressions for the intensities of the upper and lower Hubbard bands in the optical conductivity show that this spectrum is extremely sensitive on details of the ground state. The charge-density wave and superconducting phases are clearly distinguishable and even the transition to the broken-symmetry state may have a detectable influence on the conductivity.

Physical review. B, Condensed matter•Jan 15, 1997•7 citations

The Moment Sum Rule and Its Consequences for Ferromagnetism in the Hubbard Model

Michael Potthoff, T. Herrmann, Thomas Wegner +1 more

The sum rule for the moments of the spectral density is discussed for the single-band Hubbard model. It is shown that respecting the sum rule up to the order m = 3 is conceptually important for a qualitatively correct description of the quasi-particle band structure in the strong-correlation regime. Different analytical approximations for the self-energy are analyzed with respect to their compatibility with the moment sum rule. To estimate the practical usefulness of the sum rule, correlation functions and dynamical quantities are determined. The results obtained within the various approximation schemes of different complexity are compared with each other and also with essentially exact results available for infinite-dimensional lattices. It turns out that the m = 3 moment is rather unimportant for the paramagnetic phase on the hyper-cubic lattice. Contrary, it decisively influences the magnetic phase boundary as well as the critical temperature for the ferromagnetic phase on an f.c.c.-type lattice.

arXiv:cond-mat/9809212•physica status solidi (b)•Nov 1, 1998•51 citations
A variational estimate for the spin-wave velocity of the one-band Hubbard model on a square lattice in the spin-density-wave regime is studied. The estimate is given by the ratio of the f-sum rule to the static structure factor of the transverse-spin response function. The known results for the Heisenberg model are used to obtain results for those quantities in the large-U limit of the Hubbard model. The f-sum rule and static structure factor are calculated using the random-phase approximation (RPA). The spin-wave velocity calculated in the RPA, in the spin-density wave ground state, violates the variational bound.
The velocity of long-wavelength spin waves for the two-dimensional Hubbard model on a square lattice at half-filling is calculated using the variational Monte Carlo method with a Gutzwiller-type wave function. We show that the result from the Random Phase Approximation (RPA) for the spin wave velocity can also be found as the square root of the ratio of the helicity modulus and the perpendicular susceptibility as calculated in the Hartree-Fock approximation (HFA). Since the Gutzwiller wave function improves upon the HFA, our result for the spin wave velocity improves upon the RPA result. For the on-site repulsion U between 3 and 12 times the hopping integral t the spin wave velocity increases by 34 to 15% compared to the RPA result.
We study the spin-1/2 Heisenberg antiferromagnet on a square lattice using variational Monte Carlo calculations. We construct a variational wave function which gives accurate ground-state energy and is consistent with sum rules for the dynamical structure function. The spin-wave velocity and the spin-stiffness constant can be calculated using sum rules. We obtain Zc{Z}_{c}Zc​==c/c0{c}_{0}c0​, where c0{c}_{0}c0​ is the classical spin-wave velocity. This and other ground-state quantities are in good agreement with spin-wave theory and Monte Carlo calculations.
The T = 0 spin stiffness ρ s and the transverse susceptibility χ ⊥ of the square lattice half-filled Hubbard model are calculated as a function of the Hubbard parameter ratio U / t by series expansions around the Ising limit. We find that the calculated spin stiffness, transverse susceptibility, and sublattice magnetization for the Hubbard model smoothly approach the Heisenberg values for large U / t . The results are compared for different U / t with RPA and other numerical studies. The uniform susceptibility data indicate a crossover around U / t ≈ 4 between weak-coupling (spin density wave) behavior at small U and strong-coupling (Heisenberg) behavior at large U .
Dynamical spin and charge susceptibility and collective modes are studied in the framework of the random phase approximation. They are calculated from the wave function of the selfconsistently obtained ground state, including all possible higher harmonics components of the ordering vector Q . We investigate a spin wave excitation in the spin transverse mode, and phason excitation related to the domain-wall motion in the spin longitudinal and charge modes. We consider the dispersion curve of the collective mode, and discuss the dependence on the on-site U interaction and the period of the incommensurate structure.
Using the formalism introduced by Harris and Lange [Phys. Rev. 157, 295 (1967)] explicit expressions for partial sum rules of the individual Hubbard bands in the large-negative-U limit are derived. The one-particle spectrum, optical spectrum, as well as charge- and spin-response functions are considered. The approach gives a transparent description of the main features of these spectra. The main sum rules depend on only two independent nearest-neighbor expectation values which are estimated in the ground state using numerical calculations, exact results, and linear-spin-wave theory. Simple expressions for the intensities of the upper and lower Hubbard bands in the optical conductivity show that this spectrum is extremely sensitive on details of the ground state. The charge-density wave and superconducting phases are clearly distinguishable and even the transition to the broken-symmetry state may have a detectable influence on the conductivity.
The sum rule for the moments of the spectral density is discussed for the single-band Hubbard model. It is shown that respecting the sum rule up to the order m = 3 is conceptually important for a qualitatively correct description of the quasi-particle band structure in the strong-correlation regime. Different analytical approximations for the self-energy are analyzed with respect to their compatibility with the moment sum rule. To estimate the practical usefulness of the sum rule, correlation functions and dynamical quantities are determined. The results obtained within the various approximation schemes of different complexity are compared with each other and also with essentially exact results available for infinite-dimensional lattices. It turns out that the m = 3 moment is rather unimportant for the paramagnetic phase on the hyper-cubic lattice. Contrary, it decisively influences the magnetic phase boundary as well as the critical temperature for the ferromagnetic phase on an f.c.c.-type lattice.