Abstract One of the most famous quantum systems with topological properties, the spin $${{{{{{{\mathcal{S}}}}}}}}=1$$ S = 1 antiferromagnetic Heisenberg chain, is well-known to display exotic $${{{{{{{\mathcal{S}}}}}}}}=1/2$$ S = 1 / 2 edge states. However, this spin model has not been analyzed from the more general perspective of strongly correlated systems varying the electron-electron interaction strength. Here, we report the investigation of the emergence of the Haldane edge in a system of interacting electrons – the two-orbital Hubbard model—with increasing repulsion strength U and Hund interaction JH. We show that interactions not only form the magnetic moments but also form a topologically nontrivial fermionic many-body ground-state with zero-energy edge states. Specifically, upon increasing the strength of the Hubbard repulsion and Hund exchange, we identify a sharp transition point separating topologically trivial and nontrivial ground-states. Surprisingly, such a behaviour appears already at rather small values of the interaction, in a regime where the magnetic moments are barely developed.

arXiv:2304.11154Nature CommunicationsDec 22, 20238 citations

arXiv:1310.8018

Ground state of S=1 zigzag spin-orbital chain

Hiroaki Onishi

Published Oct 30, 2013• 0 citations

arXiv HTML PDF

Abstract

We investigate ground-state properties of a

t_{\rm 2g}

-orbital Hubbard model on a zigzag chain relevant for CaV

_{2}

_{4}

, by exploiting numerical techniques such as Lanczos diagonalization and density-matrix renormalization group. Assuming a V

^{3+}

ion, a local spin

S

1

state is formed by two electrons in the

t_{\rm 2g}

orbitals. That is, the system is a Haldane system with active

t_{\rm 2g}

-orbital degrees of freedom. We observe orbital-state transitions, yielding a distinct spin system under the orbital-ordered background. We also discuss the orbital structure induced by open edges, originating in the spatial anisotropy of the

t_{\rm 2g}

orbitals.

DOI: 10.48550/arxiv.1310.8018

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Abstract One of the most famous quantum systems with topological properties, the spin ${{{{{{{\mathcal{S}}}}}}}}=1$ S = 1 antiferromagnetic Heisenberg chain, is well-known to display exotic ${{{{{{{\mathcal{S}}}}}}}}=1/2$ S = 1 / 2 edge states. However, this spin model has not been analyzed from the more general perspective of strongly correlated systems varying the electron-electron interaction strength. Here, we report the investigation of the emergence of the Haldane edge in a system of interacting electrons – the two-orbital Hubbard model—with increasing repulsion strength U and Hund interaction JH. We show that interactions not only form the magnetic moments but also form a topologically nontrivial fermionic many-body ground-state with zero-energy edge states. Specifically, upon increasing the strength of the Hubbard repulsion and Hund exchange, we identify a sharp transition point separating topologically trivial and nontrivial ground-states. Surprisingly, such a behaviour appears already at rather small values of the interaction, in a regime where the magnetic moments are barely developed.Abstract One of the most famous quantum systems with topological properties, the spin $${{{{{{{\mathcal{S}}}}}}}}=1$$ S = 1 antiferromagnetic Heisenberg chain, is well-known to display exotic $${{{{{{{\mathcal{S}}}}}}}}=1/2$$ S = 1 / 2 edge states. However, this spin model has not been analyzed from the more general perspective of strongly correlated systems varying the electron-electron interaction strength. Here, we report the investigation of the emergence of the Haldane edge in a system of interacting electrons – the two-orbital Hubbard model—with increasing repulsion strength U and Hund interaction JH. We show that interactions not only form the magnetic moments but also form a topologically nontrivial fermionic many-body ground-state with zero-energy edge states. Specifically, upon increasing the strength of the Hubbard repulsion and Hund exchange, we identify a sharp transition point separating topologically trivial and nontrivial ground-states. Surprisingly, such a behaviour appears already at rather small values of the interaction, in a regime where the magnetic moments are barely developed.

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We investigate ground-state properties of a

t_{\rm 2g}

-orbital Hubbard model on a zigzag chain relevant for CaV

_{2}

_{4}

, by exploiting numerical techniques such as Lanczos diagonalization and density-matrix renormalization group. Assuming a V

^{3+}

ion, a local spin

S

1

state is formed by two electrons in the

t_{\rm 2g}

orbitals. That is, the system is a Haldane system with active

t_{\rm 2g}

t_{\rm 2g}

orbitals.

We investigate ground-state properties of a

t_{\rm 2g}

-orbital Hubbard model on a zigzag chain relevant for CaV

_{2}

_{4}

, by exploiting numerical techniques such as Lanczos diagonalization and density-matrix renormalization group. Assuming a V

^{3+}

ion, a local spin

S

1

state is formed by two electrons in the

t_{\rm 2g}

orbitals. That is, the system is a Haldane system with active

t_{\rm 2g}

t_{\rm 2g}

orbitals.

In order to clarify a key role of the orbital degree of freedom in the spin

S=1

Haldane system, we investigate ground-state properties of the

{t}_{2g}

-orbital degenerate Hubbard model on the linear chain by using numerical techniques. Increasing the Hund's rule coupling in multiorbital systems, in general, there occurs a transition from an antiferromagnetic to a ferromagnetic phase. We find that the antiferromagnetic phase is described as the Haldane system with spin gap, while in the ferromagnetic phase, there exists the gapless excitation with respect to the orbital degree of freedom. Possible relevance of the present results to actual systems is also discussed.

{\text{CaV}}_{2}{\text{O}}_{4}

and

{\text{ZnV}}_{2}{\text{O}}_{4}

are also discussed.

Abstract One of the most famous quantum systems with topological properties, the spin

{{{{{{{\mathcal{S}}}}}}}}=1

S = 1 antiferromagnetic Heisenberg chain, is well-known to display exotic

{{{{{{{\mathcal{S}}}}}}}}=1/2

S = 1 / 2 edge states. However, this spin model has not been analyzed from the more general perspective of strongly correlated systems varying the electron-electron interaction strength. Here, we report the investigation of the emergence of the Haldane edge in a system of interacting electrons – the two-orbital Hubbard model—with increasing repulsion strength U and Hund interaction JH. We show that interactions not only form the magnetic moments but also form a topologically nontrivial fermionic many-body ground-state with zero-energy edge states. Specifically, upon increasing the strength of the Hubbard repulsion and Hund exchange, we identify a sharp transition point separating topologically trivial and nontrivial ground-states. Surprisingly, such a behaviour appears already at rather small values of the interaction, in a regime where the magnetic moments are barely developed.