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

Quantum criticality of vanadium chains with strong relativistic spin-orbit interaction

Gia-Wei Chern, Natalia Borisovna Perkins, G. I. Japaridze

arXiv:1007.3472Physical Review BNov 18, 20106 citations

International Conference on Strongly Correlated Electron Systems (SCES)

Ground State of S = 1 Zigzag Spin–Orbital Chain

Hiroaki Onishi

Published Jun 16, 2014• 0 citations

Publisher

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: 10.7566/jpscp.3.014025

Related papers

Ground state of S=1 zigzag spin-orbital chain

Hiroaki Onishi

We investigate ground-state properties of a $t_{\rm 2g}$ -orbital Hubbard model on a zigzag chain relevant for CaV $_{2}$ O $_{4}$ , 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.We investigate ground-state properties of a $t_{\rm 2g}$-orbital Hubbard model on a zigzag chain relevant for CaV$_{2}$O$_{4}$, 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.

arXiv:1310.8018Oct 30, 20130 citations

Orbital-controlled magnetic transition between gapful and gapless phases in the Haldane system with t2g -orbital degeneracy

Hiroaki Onishi, Takashi Hotta

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.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.

arXiv:cond-mat/0408479Physical Review BSep 16, 20045 citations

One-dimensionalS=1 Spin–Orbital Model with Uniaxial Single-Ion Anisotropy

Satoshi Miyashita, Norio Kawakami

We investigate ground-state properties of a one-dimensional S=1 spin-orbital model with or without uniaxial single-ion anisotropy. By means of the density matrix renormalization group method, we compute the ground-state energy, the magnetization curves and the correlation functions. We discuss how the ground-state properties depend on the two exchange couplings for orbital and spin sectors. The phase diagram obtained is compared with that for the S=1/2 model. We also address the effect of uniaxial single-ion anisotropy.We investigate ground-state properties of a one-dimensional S=1 spin-orbital model with or without uniaxial single-ion anisotropy. By means of the density matrix renormalization group method, we compute the ground-state energy, the magnetization curves and the correlation functions. We discuss how the ground-state properties depend on the two exchange couplings for orbital and spin sectors. The phase diagram obtained is compared with that for the S=1/2 model. We also address the effect of uniaxial single-ion anisotropy.

arXiv:cond-mat/0412067Journal of the Physical Society of JapanFeb 15, 20054 citations

Magnetic End States in a Strongly Interacting One-Dimensional Topological Kondo Insulator

Alejandro M. Lobos, A. Dobry, Victor M. Galitski

Topological Kondo insulators are strongly correlated materials where itinerant electrons hybridize with localized spins, giving rise to a topologically nontrivial band structure. Here, we use nonperturbative bosonization and renormalization-group techniques to study theoretically a one-dimensional topological Kondo insulator, described as a Kondo-Heisenberg model, where the Heisenberg spin-1/2 chain is coupled to a Hubbard chain through a Kondo exchange interaction in the p-wave channel (i.e., a strongly correlated version of the prototypical Tamm-Schockley model). We derive and solve renormalization-group equations at two-loop order in the Kondo parameter, and find that, at half filling, the charge degrees of freedom in the Hubbard chain acquire a Mott gap, even in the case of a noninteracting conduction band (Hubbard parameter U=0). Furthermore, at low enough temperatures, the system maps onto a spin-1/2 ladder with local ferromagnetic interactions along the rungs, effectively locking the spin degrees of freedom into a spin-1 chain with frozen charge degrees of freedom. This structure behaves as a spin-1 Haldane chain, a prototypical interacting topological spin model, and features two magnetic spin-1/2 end states for chains with open boundary conditions. Our analysis allows us to derive an insightful connection between topological Kondo insulators in one spatial dimension and the well-known physics of the Haldane chain, showing that the ground state of the former is qualitatively different from the predictions of the naive mean-field theory.Topological Kondo insulators are strongly correlated materials where itinerant electrons hybridize with localized spins, giving rise to a topologically nontrivial band structure. Here, we use nonperturbative bosonization and renormalization-group techniques to study theoretically a one-dimensional topological Kondo insulator, described as a Kondo-Heisenberg model, where the Heisenberg spin-1/2 chain is coupled to a Hubbard chain through a Kondo exchange interaction in the p-wave channel (i.e., a strongly correlated version of the prototypical Tamm-Schockley model). We derive and solve renormalization-group equations at two-loop order in the Kondo parameter, and find that, at half filling, the charge degrees of freedom in the Hubbard chain acquire a Mott gap, even in the case of a noninteracting conduction band (Hubbard parameter U=0). Furthermore, at low enough temperatures, the system maps onto a spin-1/2 ladder with local ferromagnetic interactions along the rungs, effectively locking the spin degrees of freedom into a spin-1 chain with frozen charge degrees of freedom. This structure behaves as a spin-1 Haldane chain, a prototypical interacting topological spin model, and features two magnetic spin-1/2 end states for chains with open boundary conditions. Our analysis allows us to derive an insightful connection between topological Kondo insulators in one spatial dimension and the well-known physics of the Haldane chain, showing that the ground state of the former is qualitatively different from the predictions of the naive mean-field theory.

May 1, 20156 citations

Transition to the Haldane phase driven by electron-electron correlations

A. Jażdżewska, Marcin Mierzejewski, M. Środa +4 more

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.

arXiv:2304.11154Nature CommunicationsDec 22, 20238 citations

Quantum criticality of vanadium chains with strong relativistic spin-orbit interaction

Gia-Wei Chern, Natalia Borisovna Perkins, G. I. Japaridze

We study quantum phase transitions induced by the on-site spin-orbit interaction $\ensuremath{\lambda}\mathbf{L}\ensuremath{\cdot}\mathbf{S}$ in a toy model of vanadium chains. In the $\ensuremath{\lambda}\ensuremath{\rightarrow}0$ limit, the decoupled spin and orbital sectors are described by a Haldane and an Ising chain, respectively. The gapped ground state is composed of a ferro-orbital order and a spin liquid with finite correlation lengths. In the opposite limit, strong spin-orbital entanglement results in a simultaneous spin and orbital-moment ordering, which can be viewed as an orbital liquid. Using a combination of analytical arguments and density-matrix renormalization-group calculation, we show that an intermediate phase, where the ferro-orbital state is accompanied by a spin N\'eel order, is bounded on both sides by Ising transition lines. Implications for vanadium compounds ${\text{CaV}}_{2}{\text{O}}_{4}$ and ${\text{ZnV}}_{2}{\text{O}}_{4}$ are also discussed.We study quantum phase transitions induced by the on-site spin-orbit interaction $\ensuremath{\lambda}\mathbf{L}\ensuremath{\cdot}\mathbf{S}$ in a toy model of vanadium chains. In the $\ensuremath{\lambda}\ensuremath{\rightarrow}0$ limit, the decoupled spin and orbital sectors are described by a Haldane and an Ising chain, respectively. The gapped ground state is composed of a ferro-orbital order and a spin liquid with finite correlation lengths. In the opposite limit, strong spin-orbital entanglement results in a simultaneous spin and orbital-moment ordering, which can be viewed as an orbital liquid. Using a combination of analytical arguments and density-matrix renormalization-group calculation, we show that an intermediate phase, where the ferro-orbital state is accompanied by a spin N\'eel order, is bounded on both sides by Ising transition lines. Implications for vanadium compounds ${\text{CaV}}_{2}{\text{O}}_{4}$ and ${\text{ZnV}}_{2}{\text{O}}_{4}$ are also discussed.

arXiv:1007.3472Physical Review BNov 18, 20106 citations

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.

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.

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

and

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

are also discussed.