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/9707286 · Physical review. B, Condensed matter

Lattice dependence of saturated ferromagnetism in the Hubbard model

Thoralf Hanisch, Götz Silvester Uhrig, E. Müller‐Hartmann

Published Dec 1, 1997• 84 citations
arXivHTMLPDF

Abstract

We investigate the instability of the saturated ferromagnetic ground state (Nagaoka state) in the Hubbard model on various lattices in dimensions $d=2$ and $d=3$. A variational resolvent approach is developed for the Nagaoka instability both for $U=\ensuremath{\infty}$ and for $U<\ensuremath{\infty}$ which can easily be evaluated in the thermodynamic limit on all common lattices. Our results significantly improve former variational bounds for a possible Nagaoka regime in the ground-state phase diagram of the Hubbard model. We show that a pronounced particle-hole asymmetry in the density of states and a diverging density of states at the lower band edge are the most important features in order to stabilize Nagaoka ferromagnetism, particularly in the low-density limit.

DOI
10.1103/physrevb.56.13960

Related papers

Ferromagnetism in the Hubbard model: instability of the Nagaoka state on the square lattice

Th. Hanisch, E. Müller‐Hartmann

Abstract The instability of the fully polarized ferromagnetic ground state (Nagaoka state) of the Hubbard model on the square lattice is investigated. We use single spin flip variational wave functions including majority spin correlation effects and calculate spin flip energies in the thermodynamic limit. With very local wave functions and with moderate numbers of variational parameters we reproduce the best known estimate for the critical hole density δcr = 0.29 and we obtain an estimate of Ucr = 63 t for the critical coupling which is considerably better than the best estimate of Ucr = 42 t previously known. The simplicity of our wave functions makes the physical origin of the various aspects of the instability particularly transparent.

Annalen der Physik•Jan 1, 1993•41 citations

ON THE INSTABILITY OF THE FERROMAGNETIC STATE IN THE U=∞ LIMIT OF THE HUBBARD MODEL

Benoît Douçot, R. Rammal

The U=∞ limit of the Hubbard model is studied using a variational approach in which the spins are in a static coherent state. We find that the Nagaoka Ferromagnetic state is no longer the ground state as soon as two holes are present, and this for various geometries. We suggest that this instability also remains for a finite density of holes.

International Journal of Modern Physics B•Dec 1, 1989•10 citations

Stability of the Nagaoka state in the one-band Hubbard model

Guang-Shan Tian

We discuss the stability of the saturated ferromagnetic state of the one-band Hubbard model in the thermodynamic limit. We prove rigorously that the Nagaoka state is stable on a d-dimensional (d=2,3) simple-cubic lattice if the number of holes ${\mathit{N}}_{\mathit{h}}$ is less than ${\mathit{N}}_{\mathrm{\ensuremath{\Lambda}}}^{\mathrm{\ensuremath{\alpha}}}$, 0\ensuremath{\le}\ensuremath{\alpha}1/2d. Finally, we explain briefly why the Nagaoka state is probably unstable when ${\mathit{N}}_{\mathit{h}}$\ensuremath{\gg}${\mathit{N}}_{\mathrm{\ensuremath{\Lambda}}}^{1/2\mathit{d}}$.

Physical review. B, Condensed matter•Sep 1, 1991•26 citations

Ferromagnetism in the Hubbard model: instability of the Nagaoka state on the triangular, honeycomb and kagome lattices

Thoralf Hanisch, B. Kleine, Afra Ritzl +1 more

Abstract In order to analyse the lattice dependence of ferromagnetism in the two‐dimensional Hubbard model we investigate the instability of the fully polarised ferromagnetic ground state (Nagaoka state) on the triangular, honeycomb and kagome lattices. We mainly focus on the local instability, applying single spin flip variational wave functions which include majority spin correlation effects. The question of global instability and phase separation is addressed in the framework of Hartree‐Fock theory. We find a strong tendency towards Nagaoka ferromagnetism on the non‐bipartite lattices (triangular, kagome) for more than half filling. For the triangular lattice we find the Nagaoka state to be unstable above a critical density of n = 1.887 at U = ∞, thereby significantly improving former variational results. For the kagome lattice the region where ferromagnetism prevails in the phase diagram widely exceeds the flat band regime. Our results even allow the stability of the Nagaoka state in a small region below half filling. In the case of the bipartite honeycomb lattice several disconnected regions are left for a possible Nagaoka ground state.

arXiv:cond-mat/9501116•Annalen der Physik•Jan 1, 1995•56 citations

Holes in the infinite-UHubbard model: Instability of the Nagaoka state

Yan Yan Fang, Andrei E. Ruckenstein, Elbio R. Dagotto +1 more

The solution of a three-body Schr\"odinger equation (for two holes and a spin flip) shows that in the U=\ensuremath{\infty} Hubbard model the saturated ferromagnetic state with two holes is unstable (in a finite volume and for periodic boundary conditions). The ground state carries a finite momentum, and becomes degenerate with the Nagaoka state in the thermodynamic limit. This is in agreement with exact diagonalization results for small lattices where, in addition, we find that the true two-hole ground state is a singlet. As a result, our notions of ferromagnetism in the Hubbard model might need revision.

Physical review. B, Condensed matter•Oct 1, 1989•79 citations

Instability of the Nagaoka ferromagnetic state of the two-dimensional infinite-UHubbard model

Z. Song

A variational wave function with spin zero is presented for the infinite-U Hubbard model on a square lattice with the hole concentration \ensuremath{\delta}=0.5. We find that the Nagaoka ferromagnetic state is unstable for this case in the thermodynamic limit. Some discussion about this method for other hole concentrations is given.

Physical review. B, Condensed matter•Mar 1, 1994•0 citations
We investigate the instability of the saturated ferromagnetic ground state (Nagaoka state) in the Hubbard model on various lattices in dimensions d=2d=2d=2 and d=3d=3d=3. A variational resolvent approach is developed for the Nagaoka instability both for U=\ensuremath∞U=\ensuremath{\infty}U=\ensuremath∞ and for U<\ensuremath∞U<\ensuremath{\infty}U<\ensuremath∞ which can easily be evaluated in the thermodynamic limit on all common lattices. Our results significantly improve former variational bounds for a possible Nagaoka regime in the ground-state phase diagram of the Hubbard model. We show that a pronounced particle-hole asymmetry in the density of states and a diverging density of states at the lower band edge are the most important features in order to stabilize Nagaoka ferromagnetism, particularly in the low-density limit.
Abstract The instability of the fully polarized ferromagnetic ground state (Nagaoka state) of the Hubbard model on the square lattice is investigated. We use single spin flip variational wave functions including majority spin correlation effects and calculate spin flip energies in the thermodynamic limit. With very local wave functions and with moderate numbers of variational parameters we reproduce the best known estimate for the critical hole density δcr = 0.29 and we obtain an estimate of Ucr = 63 t for the critical coupling which is considerably better than the best estimate of Ucr = 42 t previously known. The simplicity of our wave functions makes the physical origin of the various aspects of the instability particularly transparent.
We discuss the stability of the saturated ferromagnetic state of the one-band Hubbard model in the thermodynamic limit. We prove rigorously that the Nagaoka state is stable on a d-dimensional (d=2,3) simple-cubic lattice if the number of holes Nh{\mathit{N}}_{\mathit{h}}Nh​ is less than ${\mathit{N}}_{\mathrm{\ensuremath{\Lambda}}}^{\mathrm{\ensuremath{\alpha}}}$, 0\ensuremath{\le}\ensuremath{\alpha}1/2d. Finally, we explain briefly why the Nagaoka state is probably unstable when Nh{\mathit{N}}_{\mathit{h}}Nh​\ensuremath{\gg}${\mathit{N}}_{\mathrm{\ensuremath{\Lambda}}}^{1/2\mathit{d}}$.
Abstract In order to analyse the lattice dependence of ferromagnetism in the two‐dimensional Hubbard model we investigate the instability of the fully polarised ferromagnetic ground state (Nagaoka state) on the triangular, honeycomb and kagome lattices. We mainly focus on the local instability, applying single spin flip variational wave functions which include majority spin correlation effects. The question of global instability and phase separation is addressed in the framework of Hartree‐Fock theory. We find a strong tendency towards Nagaoka ferromagnetism on the non‐bipartite lattices (triangular, kagome) for more than half filling. For the triangular lattice we find the Nagaoka state to be unstable above a critical density of n = 1.887 at U = ∞, thereby significantly improving former variational results. For the kagome lattice the region where ferromagnetism prevails in the phase diagram widely exceeds the flat band regime. Our results even allow the stability of the Nagaoka state in a small region below half filling. In the case of the bipartite honeycomb lattice several disconnected regions are left for a possible Nagaoka ground state.
The solution of a three-body Schr\"odinger equation (for two holes and a spin flip) shows that in the U=\ensuremath{\infty} Hubbard model the saturated ferromagnetic state with two holes is unstable (in a finite volume and for periodic boundary conditions). The ground state carries a finite momentum, and becomes degenerate with the Nagaoka state in the thermodynamic limit. This is in agreement with exact diagonalization results for small lattices where, in addition, we find that the true two-hole ground state is a singlet. As a result, our notions of ferromagnetism in the Hubbard model might need revision.