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

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 ( I = a, 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 wen 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.

Ground-state and finite-temperature signatures of quantum phase transitions in the half-filled Hubbard model on a honeycomb lattice

“…[7] As with the square lattice Hubbard model, Nagaoka lattice at strong couplings (U/t > 12), as has been investigated by Hirsch using exact diagonalization on small clusters [8] and by Hanisch et al using Gutzwiller wave functions. [9] We conclude this introduction by noting that the Hubbard model on a honeycomb lattice has also been suggested to be of interest for a variety of systems including graphite sheets, [4] and carbon nanotubes [10], as well as MgB 2 [6] and Pb and Sn on Ge(111) surfaces.…”

Phase diagram and magnetic collective excitations of the Hubbard model for graphene sheets and layers

“…The triangular, the honeycomb, and the Kagomé lattices were studied, but a strong tendency for a Nagaoka type ground state was found only in nonbipartite lattices (triangular and Kagome). 12 On the other hand, the effect of long range interactions in half-filled sheets of graphite was considered from a mean field point of view, using an extended Hubbard model. A large region of the phase diagram having a charge density wave ground state was found.…”

Ferromagnetism in the Two Dimensionalt−t′Hubbard Model at the Van Hove Density

“…The results turned out to be strongly dependent on the quasiparticle spectrum [3], and, generically, unrealistically large U were required to stabilize a fully polarized state. Motivated by the recent proofs of FM in certain models with flat bands [4], in this Letter we take a complementary route, investigating the stability of the paramagnetic phase of a model with a high density of states against FM at weak coupling.…”

“…Motivated by an exact result of Nagaoka [2], most papers studied the stability of a fully polarized state (believed to occur in the phase diagram of the Hubbard model at large interaction strength and close to half filling) against single spin flips. The results turned out to be strongly dependent on the quasiparticle spectrum [3], and, generically, unrealistically large U were required to stabilize a fully polarized state. Motivated by the recent proofs of FM in certain models with flat bands [4], in this Letter we take a complementary route, investigating the stability of the paramagnetic phase of a model with a high density of states against FM at weak coupling.…”