Failure of Saturated Ferromagnetism for the Hubbard Model with Two Holes

An extension is given of Nagaoka's theorem on the existence of ferromagnetism in the large-U Hubbard model with precisely one hole. The present extension covers a large class of models with arbitrary non-negative hopping matrix elements and arbitrary spin-independent interactions.

Physical review. B, Condensed matterNov 1, 1989194 citations

Ferromagnetism in Hubbard Chains

Mario Cuoco, Canio Noce, Alfonso Romano

We analyze the possible occurrence of ferromagnetism in the Hubbard model, by means of an exact diagonalization study performed on 3-to 8-site chains with periodic boundary conditions.In the case of one hole in the half-filled configuration, we find that the Nagaoka state is reached only in the 3-and in the 4-site case.Ground states characterized by unsaturated ferromagnetism are found when the case of more than one hole is considered.

Acta Physica Polonica AFeb 1, 19970 citations

Failure of Saturated Ferromagnetism for the Hubbard Model with Two Holes

Lint Toth

Published Jan 1, 1991• 0 citations

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Abstract

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Failure of saturated ferromagnetism for the Hubbard model with two holes

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We consider the Hubbard model on a finite set of sites with nonpositive hopping matrix elements and infinitely strong on-site repulsion. Nagaoka's theorem states that in this model the relative ground state in the sector with one unoccupied site is maximally ferromagnetic. We show that this phenomenon is a consequence of a combinatorial coincidence valid in the one-hole regime only. In the case of more than one hole there is no reason to expect maximally ferromagnetic ground states. We prove this claim for the case of two holes for models defined on a class of graphs which contains all tori that are not too small.We consider the Hubbard model on a finite set of sites with nonpositive hopping matrix elements and infinitely strong on-site repulsion. Nagaoka's theorem states that in this model the relative ground state in the sector with one unoccupied site is maximally ferromagnetic. We show that this phenomenon is a consequence of a combinatorial coincidence valid in the one-hole regime only. In the case of more than one hole there is no reason to expect maximally ferromagnetic ground states. We prove this claim for the case of two holes for models defined on a class of graphs which contains all tori that are not too small.

Jan 1, 19910 citations

Balance and frustration in strongly correlated itinerant electron systems: An extension of Nagaoka's theorem

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We prove that Nagaoka's theorem, that the ground state of the large- $U$ Hubbard model with exactly one hole is ferromagnetic, holds for any balanced Hamiltonian. We argue that, in itinerant electron systems, a balanced Hamiltonian, rather than bipartite lattice, defines an unfrustrated system. The proof is valid for multiorbital models with arbitrary two-orbital interactions provided that no exchange interactions are antiferromagnetic: a class of models including the Kanomori Hamiltonian.We prove that Nagaoka's theorem, that the ground state of the large-$U$ Hubbard model with exactly one hole is ferromagnetic, holds for any balanced Hamiltonian. We argue that, in itinerant electron systems, a balanced Hamiltonian, rather than bipartite lattice, defines an unfrustrated system. The proof is valid for multiorbital models with arbitrary two-orbital interactions provided that no exchange interactions are antiferromagnetic: a class of models including the Kanomori Hamiltonian.

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Nagaoka Ferromagnetism in Two-Band Hubbard Model

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In the present paper, we investigate the existence of ferromagnetism in a two-band Hubbard model, by applying a recently-introduced method by us to study ferromagnetism in metallic clusters. We prove rigorously that the ground state of this model is ferromagnetic if the intra-orbital Coulomb repulsion between electrons is infinitely strong and only one hole exists in the system. Our theorem improves a previous result. Furthermore, our method can also be applied to deal with the case of multiple holes.In the present paper, we investigate the existence of ferromagnetism in a two-band Hubbard model, by applying a recently-introduced method by us to study ferromagnetism in metallic clusters. We prove rigorously that the ground state of this model is ferromagnetic if the intra-orbital Coulomb repulsion between electrons is infinitely strong and only one hole exists in the system. Our theorem improves a previous result. Furthermore, our method can also be applied to deal with the case of multiple holes.

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Ferromagnetic domains in the large- $U$ Hubbard model with a few holes: an FCIQMC studyFerromagnetic domains in the large-$U$ Hubbard model with a few holes: an FCIQMC study

Yun, Sujun, Werner Dobrautz, Luo Hongjun +3 more

Two-dimensional Hubbard lattices with two or three holes are investigated as a function of $U$ in the large- $U$ limit. In the so-called Nagaoka limit (one-hole system at infinite $U$ ), it is known that the Hubbard model exhibits a ferromagnetic ground-state. Here, by means of exact FCIQMC simulations applied to periodic lattices up to 24 sites, we compute spin-spin correlation functions as a function of increasing $U$ . The correlation functions clearly demonstrate the onset of ferromagnetic domains, centred on individual holes. The overall total spin of the wavefunctions remain the lowest possible (0, or $\frac{1}{2}$ , depending on the number of holes). The ferromagnetic domains appear at interaction strengths comparable to the critical interaction strengths of the Nagaoka transition in finite systems with strictly one hole. The existence of such ferromagnetic domains is the signature of Nagaoka physics in Hubbard systems with a small (but greater than one) number of holes.Two-dimensional Hubbard lattices with two or three holes are investigated as a function of $U$ in the large-$U$ limit. In the so-called Nagaoka limit (one-hole system at infinite $U$), it is known that the Hubbard model exhibits a ferromagnetic ground-state. Here, by means of exact FCIQMC simulations applied to periodic lattices up to 24 sites, we compute spin-spin correlation functions as a function of increasing $U$. The correlation functions clearly demonstrate the onset of ferromagnetic domains, centred on individual holes. The overall total spin of the wavefunctions remain the lowest possible (0, or $\frac{1}{2}$, depending on the number of holes). The ferromagnetic domains appear at interaction strengths comparable to the critical interaction strengths of the Nagaoka transition in finite systems with strictly one hole. The existence of such ferromagnetic domains is the signature of Nagaoka physics in Hubbard systems with a small (but greater than one) number of holes.

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Extension of Nagaoka’s theorem on the large- U Hubbard model

Hal Tasaki

Physical review. B, Condensed matterNov 1, 1989194 citations

Ferromagnetism in Hubbard Chains

Mario Cuoco, Canio Noce, Alfonso Romano

Acta Physica Polonica AFeb 1, 19970 citations

We prove that Nagaoka's theorem, that the ground state of the large-

U

Hubbard model with exactly one hole is ferromagnetic, holds for any balanced Hamiltonian. We argue that, in itinerant electron systems, a balanced Hamiltonian, rather than bipartite lattice, defines an unfrustrated system. The proof is valid for multiorbital models with arbitrary two-orbital interactions provided that no exchange interactions are antiferromagnetic: a class of models including the Kanomori Hamiltonian.

Ferromagnetic domains in the large-

U

Hubbard model with a few holes: an FCIQMC study

Two-dimensional Hubbard lattices with two or three holes are investigated as a function of

U

in the large-

U

limit. In the so-called Nagaoka limit (one-hole system at infinite

U

), it is known that the Hubbard model exhibits a ferromagnetic ground-state. Here, by means of exact FCIQMC simulations applied to periodic lattices up to 24 sites, we compute spin-spin correlation functions as a function of increasing

U

. The correlation functions clearly demonstrate the onset of ferromagnetic domains, centred on individual holes. The overall total spin of the wavefunctions remain the lowest possible (0, or

\frac{1}{2}

, depending on the number of holes). The ferromagnetic domains appear at interaction strengths comparable to the critical interaction strengths of the Nagaoka transition in finite systems with strictly one hole. The existence of such ferromagnetic domains is the signature of Nagaoka physics in Hubbard systems with a small (but greater than one) number of holes.