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

Variational study of the stability of the Nagaoka state against single-spin flips in the two-dimensional t−t′ Hubbard model

Michal Bajdich, R. Hlubina

Published May 29, 2001• 0 citations
Publisher

Abstract

Making use of variational wave functions of the Basile-Elser type we study the stability of the Nagaoka state against single-spin flips in the two-dimensional $t\ensuremath{-}{t}^{\ensuremath{'}}$ Hubbard model for ${t}^{\ensuremath{'}}/t\ensuremath{\sim}0.5.$ In the low-density limit the variational estimate of the stability region of the Nagaoka state is in qualitative agreement with the predictions of the T-matrix approximation.

DOI
10.1103/physrevb.63.233105

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

Ferromagnetism in the Hubbard model: Spin waves and instability of the Nagaoka state

P. Wurth, E. Müller‐Hartmann

Abstract We discuss two single spin flip variational wave functions describing spin wave excitations which were proposed earlier by Shastry, Krishnamurthy and Anderson (SKA) and by Basile and Elser (BE), respectively, in order to investigate the instability of the fully polarized ferromagnetic state (Nagaoka state) in the infinite U Hubbard model. We calculate the energy of these variational states for the square lattice and for multiple chains. At the zone boundary in the vicinity of the point (0, π) the spin wave energy is reduced substantially by the binding of the spin up hole to the flipped down spin. For the square lattice this leads to a critical hole density of δcr = 0.407 for the SKA spin wave and of δcr = 0.322 for the BE spin wave which implies remarkable improvements in comparison to the corresponding scattering states investigated previously.

Annalen der Physik•Jan 1, 1995•13 citations

Ferromagnetism in the Hubbard model on the square lattice: Improved instability criterion for the Nagaoka state

P. Wurth, Götz Silvester Uhrig, E. Müller‐Hartmann

Abstract The instability of the fully polarized ferromagnetic state (Nagaoka state) with respect to single spin flips is re‐examined for the Hubbard model on the square lattice with a large family of variational wave functions which include correlation effects of the majority spins in the vicinity of the flipped spin. We find a critical hole density of δcr = 0.251 for U = ∞ and a critical coupling of Ucr = 77.7t. Both values improve previous variational results considerably.

arXiv:cond-mat/9512060•Annalen der Physik•Mar 1, 1996•39 citations

Single spin flip in the Nagaoka state: Problems with the Gutzwiller wave function

Thilo Kopp, Andrei E. Ruckenstein, Stefan Schmitt-Rink

We reconsider the problem of a single spin flip in the saturated ferromagnetic state (the Nagaoka state) of the infinite-U Hubbard model for a small (but finite) hole concentration. By studying the ground-state energy and the spin-flip spectral function, we argue that recently proposed Gutzwiller-like variational wave functions are not appropriate for studying this problem in one and two dimensions.

Physical review. B, Condensed matter•Oct 1, 1990•26 citations

One-flipped-spin sector of the Hubbard model: A search for non-Fermi-liquid behavior

David M. Frenkel

One flipped spin in the spin-polarized sector of the Hubbard model away from half-filling is considered. Aspects other than stability of the Nagaoka solution or viability of the Gutzwiller approximation (considered previously by other authors) are focused on. It is argued that understanding the phase-coherence properties of the flipped spin may be a good starting point in an attempt to prove or disprove the violation of the Fermi-liquid-like behavior in the two-dimensional (2D) Hubbard model, an outcome that has been strongly advocated by P. W. Anderson. The system is analyzed in the weak-coupling limit via a variational wave function in 1D and 2D. The variational problem is reduced to solving a nonlinear Schr\"odinger equation in both of these dimensionalities. It is found that a solitonic type of solution emerges in weak coupling in 1D, but not in 2D. This implies a conventional Fermi-liquid-like behavior in our system in 2D in the weak-coupling limit. A discussion of possible loopholes in our approach is presented, and the remaining possibility of non-Fermi-liquid-like behavior in the strong-coupling limit at finite densities in 2D is noted. An interesting connection with the existing work on heavy mobile impurities in metals and in $^{3}\mathrm{He}$ is pointed out.

Physical review. B, Condensed matter•Dec 15, 1992•11 citations

Lattice dependence of saturated ferromagnetism in the Hubbard model

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

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.

arXiv:cond-mat/9707286•Physical review. B, Condensed matter•Dec 1, 1997•84 citations
Making use of variational wave functions of the Basile-Elser type we study the stability of the Nagaoka state against single-spin flips in the two-dimensional t\ensuremath−t\ensuremath′t\ensuremath{-}{t}^{\ensuremath{'}}t\ensuremath−t\ensuremath′ Hubbard model for t\ensuremath′/t\ensuremath∼0.5.{t}^{\ensuremath{'}}/t\ensuremath{\sim}0.5.t\ensuremath′/t\ensuremath∼0.5. In the low-density limit the variational estimate of the stability region of the Nagaoka state is in qualitative agreement with the predictions of the T-matrix approximation.
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.
Abstract We discuss two single spin flip variational wave functions describing spin wave excitations which were proposed earlier by Shastry, Krishnamurthy and Anderson (SKA) and by Basile and Elser (BE), respectively, in order to investigate the instability of the fully polarized ferromagnetic state (Nagaoka state) in the infinite U Hubbard model. We calculate the energy of these variational states for the square lattice and for multiple chains. At the zone boundary in the vicinity of the point (0, π) the spin wave energy is reduced substantially by the binding of the spin up hole to the flipped down spin. For the square lattice this leads to a critical hole density of δcr = 0.407 for the SKA spin wave and of δcr = 0.322 for the BE spin wave which implies remarkable improvements in comparison to the corresponding scattering states investigated previously.
One flipped spin in the spin-polarized sector of the Hubbard model away from half-filling is considered. Aspects other than stability of the Nagaoka solution or viability of the Gutzwiller approximation (considered previously by other authors) are focused on. It is argued that understanding the phase-coherence properties of the flipped spin may be a good starting point in an attempt to prove or disprove the violation of the Fermi-liquid-like behavior in the two-dimensional (2D) Hubbard model, an outcome that has been strongly advocated by P. W. Anderson. The system is analyzed in the weak-coupling limit via a variational wave function in 1D and 2D. The variational problem is reduced to solving a nonlinear Schr\"odinger equation in both of these dimensionalities. It is found that a solitonic type of solution emerges in weak coupling in 1D, but not in 2D. This implies a conventional Fermi-liquid-like behavior in our system in 2D in the weak-coupling limit. A discussion of possible loopholes in our approach is presented, and the remaining possibility of non-Fermi-liquid-like behavior in the strong-coupling limit at finite densities in 2D is noted. An interesting connection with the existing work on heavy mobile impurities in metals and in 3He^{3}\mathrm{He}3He is pointed out.
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 $U=\ensuremath{\infty}$ 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.