In this work, the ground states of the Hubbard model on complete graph are studied, for a finite lattice size $L$ and arbitrary on-site energy $U$ . We construct explicitly the ground states of the system when the number of the electrons $N_e \ge L+1$ . In particular, for $N_e=L+1$ , the ground state is ferromagnetic with total spin $s_g=(N_e-2)/2$ .In this work, the ground states of the Hubbard model on complete graph are studied, for a finite lattice size $L$ and arbitrary on-site energy $U$. We construct explicitly the ground states of the system when the number of the electrons $N_e \ge L+1$. In particular, for $N_e=L+1$, the ground state is ferromagnetic with total spin $s_g=(N_e-2)/2$.

arXiv:cond-mat/9604121Apr 18, 19961 citation

Effects of van Hove singularities on magnetism and superconductivity in the t − t ′ Hubbard model: A parquet approach

V. Yu. Irkhin, A. A. Katanin, Mikhail I. Katsnelson

The $t\ensuremath{-}{t}^{\ensuremath{'}}$ Hubbard model for the Fermi level near the van Hove singularity is considered within the renormalization group and parquet approaches. Interplay of ferromagnetic, antiferromagnetic, and superconducting channels is investigated, and the phase diagram of the model is constructed. In comparison with previous approaches, the account of ferromagnetic fluctuations suppresses superconducting pairing and, vice versa, the influence of the Cooper channel decreases the Curie temperature, so that the Stoner criterion is inapplicable even qualitatively.The $t\ensuremath{-}{t}^{\ensuremath{'}}$ Hubbard model for the Fermi level near the van Hove singularity is considered within the renormalization group and parquet approaches. Interplay of ferromagnetic, antiferromagnetic, and superconducting channels is investigated, and the phase diagram of the model is constructed. In comparison with previous approaches, the account of ferromagnetic fluctuations suppresses superconducting pairing and, vice versa, the influence of the Cooper channel decreases the Curie temperature, so that the Stoner criterion is inapplicable even qualitatively.

arXiv:cond-mat/0102381Physical review. B, Condensed matterOct 3, 200196 citations

Ferromagnetism in the Hubbard Model

Wolfgang Nolting, Michael Potthoff, T. Herrmann +1 more

arXiv:cond-mat/0107255Lecture notes in physicsJan 1, 20015 citations

Describing ferromagnetism in the Hubbard model

Ben Hur Bernhard

Journal of Magnetism and Magnetic MaterialsMar 7, 20084 citations

Auxiliary-space variational approach for theU=∞ Hubbard model: The stability of a ferromagnetic state

V. Ya. Krivnov, А. А. Овчинников

A variational approach has been used to study the stability of the Nagaoka state in the Hubbard model with infinite interaction. In this approach, real Fermi operators are replaced by auxiliary ones; an effective Hamiltonian is constructed in terms of these auxiliary operators. A two-chain (ladder) system is considered as an example. For this model, we show that the Nagaoka state is unstable with respect to the creation of two-phase states: ferromagnetic and singlet spin states. The instability occurs at a finite density of holes.A variational approach has been used to study the stability of the Nagaoka state in the Hubbard model with infinite interaction. In this approach, real Fermi operators are replaced by auxiliary ones; an effective Hamiltonian is constructed in terms of these auxiliary operators. A two-chain (ladder) system is considered as an example. For this model, we show that the Nagaoka state is unstable with respect to the creation of two-phase states: ferromagnetic and singlet spin states. The instability occurs at a finite density of holes.

Physical review. B, Condensed matterJun 1, 19926 citations

In this work, the ground states of the Hubbard model on complete graph are studied, for a finite lattice size

L

and arbitrary on-site energy

U

. We construct explicitly the ground states of the system when the number of the electrons

N_e \ge L+1

. In particular, for

N_e=L+1

, the ground state is ferromagnetic with total spin

s_g=(N_e-2)/2