We consider magnetic instabilities in the two-dimensional Hubbard model at small doping. We find that the renormalization of the effective interaction prevents an immediate instability of a commensurate antiferromagnetic state upon doping. At increased doping levels, our calculations indicate the occurrence of an instability in the channel of transverse spin fluctuations. This instability is known to lead to a spiral magnetic phase. We also consider a dynamical spin susceptibility near the instability and find that conventional spin waves play no role in the transition. Instead, the incommensurate instability is governed by collective fermionic excitations coupled to the spin background.We consider magnetic instabilities in the two-dimensional Hubbard model at small doping. We find that the renormalization of the effective interaction prevents an immediate instability of a commensurate antiferromagnetic state upon doping. At increased doping levels, our calculations indicate the occurrence of an instability in the channel of transverse spin fluctuations. This instability is known to lead to a spiral magnetic phase. We also consider a dynamical spin susceptibility near the instability and find that conventional spin waves play no role in the transition. Instead, the incommensurate instability is governed by collective fermionic excitations coupled to the spin background.

Physical review. B, Condensed matterNov 1, 1992115 citations

Doped Hubbard antiferromagnet: Instability and effective interactions

Avinash Singh, Zlatko Tešanović, Ju H. Kim

The homogeneous Hartree-Fock antiferromagnetic (AF) state of the doped Hubbard model is shown to be unstable for infinitesimal doping concentration. Driven by long-wavelength intraband fluctuations, this instability with respect to infinitesimal fluctuations around the mean-field state is inferred from the nature of the static spin response, which increases away from the AF wave vector (\ensuremath{\pi},\ensuremath{\pi}). The effective interaction between antiparallel-spin holes in the lower band is found to contain a short-range attractive component, with an energy scale Jx. We discuss the crossover of the characteristic length scale for intraband fluctuations from the antiferromagnetic state to the spiral state, also unstable for infinitesimal doping concentration.The homogeneous Hartree-Fock antiferromagnetic (AF) state of the doped Hubbard model is shown to be unstable for infinitesimal doping concentration. Driven by long-wavelength intraband fluctuations, this instability with respect to infinitesimal fluctuations around the mean-field state is inferred from the nature of the static spin response, which increases away from the AF wave vector (\ensuremath{\pi},\ensuremath{\pi}). The effective interaction between antiparallel-spin holes in the lower band is found to contain a short-range attractive component, with an energy scale Jx. We discuss the crossover of the characteristic length scale for intraband fluctuations from the antiferromagnetic state to the spiral state, also unstable for infinitesimal doping concentration.

Physical review. B, Condensed matterOct 1, 199123 citations

Stability Analysis of the Hubbard Model

I. Grote, Elmar G. Körding, Franz Wegner

arXiv:cond-mat/0106604Journal of Low Temperature PhysicsFeb 1, 200261 citations

Exact Nagaoka-to-spiral transition in the doped infinite-U triangular lattice

Yang Zhang, Cristian D. Batista

We study the single-hole infinite- $U$ Hubbard model on the triangular lattice with nearest- and next-nearest-neighbor hoppings $t_1$ and $t_2$ . A frustrating $t_2$ destabilizes Nagaoka ferromagnetism through a Lifshitz transition to a long-wavelength coplanar spiral at $t_{2,c}/t_1=-0.182$ . We determine the critical point analytically by reducing the many-body problem to an effective two-body hole--magnon scattering problem in which the hard-core hole--magnon constraint is treated exactly. Numerical calculations confirm the spiral ground state and reveal a coherent spin polaron with quasiparticle weight $Z\simeq0.92$ at the Lifshitz-shifted momentum $\mathbf{K}=-\mathbf{Q}^*$ . These results establish the first quantum instability of the triangular-lattice Nagaoka ferromagnet and provide the magnetic baseline for magnon-mediated pairing at finite doping.We study the single-hole infinite-$U$ Hubbard model on the triangular lattice with nearest- and next-nearest-neighbor hoppings $t_1$ and $t_2$. A frustrating $t_2$ destabilizes Nagaoka ferromagnetism through a Lifshitz transition to a long-wavelength coplanar spiral at $t_{2,c}/t_1=-0.182$. We determine the critical point analytically by reducing the many-body problem to an effective two-body hole--magnon scattering problem in which the hard-core hole--magnon constraint is treated exactly. Numerical calculations confirm the spiral ground state and reveal a coherent spin polaron with quasiparticle weight $Z\simeq0.92$ at the Lifshitz-shifted momentum $\mathbf{K}=-\mathbf{Q}^*$. These results establish the first quantum instability of the triangular-lattice Nagaoka ferromagnet and provide the magnetic baseline for magnon-mediated pairing at finite doping.

arXiv:2607.20726Jul 22, 20260 citations

We study the single-hole infinite-

U

Hubbard model on the triangular lattice with nearest- and next-nearest-neighbor hoppings

t_1

and

t_2

. A frustrating

t_2

destabilizes Nagaoka ferromagnetism through a Lifshitz transition to a long-wavelength coplanar spiral at

t_{2,c}/t_1=-0.182

. We determine the critical point analytically by reducing the many-body problem to an effective two-body hole--magnon scattering problem in which the hard-core hole--magnon constraint is treated exactly. Numerical calculations confirm the spiral ground state and reveal a coherent spin polaron with quasiparticle weight

Z\simeq0.92

at the Lifshitz-shifted momentum

\mathbf{K}=-\mathbf{Q}^*

. These results establish the first quantum instability of the triangular-lattice Nagaoka ferromagnet and provide the magnetic baseline for magnon-mediated pairing at finite doping.