Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2211.05354 · Journal of the Physical Society of Japan

Enhanced Spin–Orbit Coupling in a Correlated Metal

Katsunori Kubo

Published Nov 10, 2022• 5 citations
arXivHTMLPDF

Abstract

We investigate the correlation effects on spin-orbit coupling (SOC) in a two-orbital Hubbard model on a square lattice by applying the variational Monte Carlo method. We consider an effective SOC constant $λ_{\text{eff}}$ in the one-body part of the variational wave function and mainly discuss the cases of the electron number per site $n=1$, that is, quarter filling. We find that $λ_{\text{eff}}$ is proportional to the bare value $λ$ and depends on the electron-electron interactions through $(U'-J')$ in a relatively wide parameter range in the paramagnetic (PM) phase, where $U'$ is the interorbital Coulomb interaction and $J'$ is the pair hopping interaction. Increasing the electron-electron interactions in the PM phase leads to a transition to an effective one-band state, in which the upper band becomes empty due to the enhanced $λ_{\text{eff}}$. We also construct phase diagrams considering magnetic order. The carrier doping effect on $λ_{\text{eff}}$ is also investigated. We find that $λ_{\text{eff}}$ enhances in a strongly correlated region around the Mott transition point and it is necessary to include the correlation effects beyond the Hartree-Fock approximation to describe the enhanced SOC properly.

DOI
10.7566/jpsj.91.124707

Related papers

Enhancement of an Effective Spin–Orbit Coupling in a Correlated Metal

Katsunori Kubo

To discuss correlation effects on the spin-orbit coupling (SOC), we investigate a two-orbital Hubbard model with SOC on a square lattice by using the variational Monte Carlo method.In the variational wave function, we consider an effective SOC constant λ eff in the one-body part of the variational wave function.In addition to the Gutzwiller parameters and doublon-holon binding factors, which describe correlation effects beyond the Hartree-Fock approximation, λ eff is treated as a variational parameter.We find that λ eff increases from the bare value by the Coulomb interaction.While the enhancement of λ eff is strongly suppressed in comparison with the result of the Hartree-Fock approximation, we find that λ eff can still become several times larger than the bare value.

International Conference on Low Temperature Physics (LT)•May 22, 2023•1 citation

Variational Monte Carlo Study of Two-Dimensional Multi-Orbital Hubbard Model on Square Lattice

Y Takenaka, N. Kawakami

We investigate the Mott transition in a two-dimensional two-orbital Hubbard model on a square lattice at half filling by using the variational Monte Carlo method. As a variational trial wave function, we consider Gutzwiller's on-site correlations and nearest-neighbor doublon-holon correlations. We calculate the ground-state energy and the other physical quantities, all of which clearly signal a first-order Mott transition. We thus obtain the phase diagram at zero temperature, where we find the coexistence region of the metal and the Mott insulator. We discuss how Hund's coupling affects the nature of the Mott transition in this system.

Journal of Physics Conference Series•Dec 17, 2012•5 citations

Assessing the orbital selective Mott transition with variational wave functions

Luca F. Tocchio, Federico Arrigoni, Sandro Sorella +1 more

We study the Mott metal-insulator transition in the two-band Hubbard model with different hopping amplitudes t1 and t2 for the two orbitals on the two-dimensional square lattice by using non-magnetic variational wave functions, similarly to what has been considered in the limit of infinite dimensions by dynamical mean-field theory. We work out the phase diagram at half filling (i.e. two electrons per site) as a function of R = t2/t1 and the on-site Coulomb repulsion U, for two values of the Hund's coupling J = 0 and J/U = 0.1. Our results are in good agreement with previous dynamical mean-field theory calculations, demonstrating that the non-magnetic phase diagram is only slightly modified from infinite to two spatial dimensions. Three phases are present: a metallic one, for small values of U, where both orbitals are itinerant; a Mott insulator, for large values of U, where both orbitals are localized because of the Coulomb repulsion; and the so-called orbital-selective Mott insulator (OSMI), for small values of R and intermediate Us, where one orbital is localized while the other one is still itinerant. The effect of the Hund's coupling is two-fold: on one side, it favors the full Mott phase over the OSMI; on the other side, it stabilizes the OSMI at larger values of R.

arXiv:1505.07006•Journal of Physics Condensed Matter•Feb 16, 2016•16 citations

Two-dimensional extended Hubbard model: doping, next-nearest neighbor hopping and phase diagrams

A. Sherman

Abstract Using the strong coupling diagram technique, we investigate the extended Hubbard model on a two-dimensional square lattice. This approach allows for charge and spin fluctuations and a short-range antiferromagnetic order at nonzero temperatures. The model features the first-order phase transition to states with alternating site occupations (SAO) at the intersite repulsion v = v c . In this work, we show that doping decreases v c . For a nonzero next-nearest neighbor hopping t ′ , less mobile carriers produce a stronger fall in v c . For half-filling and t ′ = 0 , we consider phase diagrams for a fixed temperature T, on-site U, and intersite repulsions. The diagrams contain regions of SAO, Mott insulator, and several metallic states distinguished by their densities of states. Two of them are characterized by a dip and a peak at the Fermi level. The dip originates from the Slater mechanism for itinerant electrons, while the peak to bound states of electrons with localized magnetic moments. The existence of these two metallic regions in the phase diagram is a manifestation of the Pomeranchuk effect. The boundary between these regions reveals itself as a kink in the curve v c (T) and as a maximum in the T dependence of the double occupancy D. Our calculated D for different values of v, U, and T are in semiquantitative agreement with Monte Carlo results.

arXiv:2304.14683•Physica Scripta•Oct 4, 2023•8 citations

Ground state of a three-band Hubbard model with Hund’s coupling: Janus-faced behavior in presence of magnetic order

Arun Kumar Maurya, Md. Tahir Hossain Sarder, Amal Medhi

Abstract We study the ground state of the three-band degenerate Hubbard model on a square lattice at integer fillings using the variational slave-spin mean field method. At half-filling, the method reproduces the well known result that the ground state is antiferromagnetic (AF) insulating at smaller values of Hubbard onsite repulsion U , while it becomes Mott insulating with Néel AF order at higher U . Away from half-filling, for two particles per site, we show that the model supports a ferromagnetic (FM) metallic state with fully polarized spins at sufficiently large U . The FM state occurs irrespective of the value of Hund’s coupling J . The ferromagnetism at J = 0 can be explained by the Stoner mechanism while that for J > 0 is shown to arise from the superexchange process. At this band filling, the Hund’s coupling J is known to have the Janus-faced effect on electronic correlations where it enhances correlations at smaller U while reducing it at higher U . We show that these two effects are separated by the paramagnetic (PM) to FM transition point. The former effect is obtained at the PM state while the latter occurs in the FM state. The FM phase also occurs for one particle per site but here Hund’s coupling J reduces the effect of electronic correlations at all U .

Journal of Physics Condensed Matter•Jul 23, 2021•3 citations

Effect of Spin Correlations on Multi-orbital Metal-Insulator Transitions and Suppression of Orbital Selective Mott Transitions

Ya‐Min Quan, Liang‐Jian Zou, Hai‐Qing Lin

We present the influence of spin correlation on the metal-insulator transitions (MIT) in two-orbital Hubbard models by the Kotliar-Ruckenstein slave-boson approach. In the asymmetric half-filling situation, the two orbits simultaneously transit from conducting to insulating states with the increase of Coulomb correlation, accompanied by a paramagnetic (PM)-antiferromagnetic (AFM) transition. The orbital selective Mott transition found in the PM condition is completely suppressed over a wide correlation range, though it may exist in the systems away from half-filling. In the insulating state, the system crosses over from a partially-polarized spin-gapped phase in the intermediate correlation regime to an almost fully-polarized Mott insulating phase in the strong correlation regime. These results demonstrate that the spin modulation to the quasiparticle spectra brings much rich and more interesting MIT scenario in multi-orbital correlated systems.

arXiv:1105.4913•May 25, 2011•0 citations
We investigate the correlation effects on spin-orbit coupling (SOC) in a two-orbital Hubbard model on a square lattice by applying the variational Monte Carlo method. We consider an effective SOC constant λeffλ_{\text{eff}}λeff​ in the one-body part of the variational wave function and mainly discuss the cases of the electron number per site n=1n=1n=1, that is, quarter filling. We find that λeffλ_{\text{eff}}λeff​ is proportional to the bare value λλλ and depends on the electron-electron interactions through (U′−J′)(U'-J')(U′−J′) in a relatively wide parameter range in the paramagnetic (PM) phase, where U′U'U′ is the interorbital Coulomb interaction and J′J'J′ is the pair hopping interaction. Increasing the electron-electron interactions in the PM phase leads to a transition to an effective one-band state, in which the upper band becomes empty due to the enhanced λeffλ_{\text{eff}}λeff​. We also construct phase diagrams considering magnetic order. The carrier doping effect on λeffλ_{\text{eff}}λeff​ is also investigated. We find that λeffλ_{\text{eff}}λeff​ enhances in a strongly correlated region around the Mott transition point and it is necessary to include the correlation effects beyond the Hartree-Fock approximation to describe the enhanced SOC properly.
To discuss correlation effects on the spin-orbit coupling (SOC), we investigate a two-orbital Hubbard model with SOC on a square lattice by using the variational Monte Carlo method.In the variational wave function, we consider an effective SOC constant λ eff in the one-body part of the variational wave function.In addition to the Gutzwiller parameters and doublon-holon binding factors, which describe correlation effects beyond the Hartree-Fock approximation, λ eff is treated as a variational parameter.We find that λ eff increases from the bare value by the Coulomb interaction.While the enhancement of λ eff is strongly suppressed in comparison with the result of the Hartree-Fock approximation, we find that λ eff can still become several times larger than the bare value.
We investigate the Mott transition in a two-dimensional two-orbital Hubbard model on a square lattice at half filling by using the variational Monte Carlo method. As a variational trial wave function, we consider Gutzwiller's on-site correlations and nearest-neighbor doublon-holon correlations. We calculate the ground-state energy and the other physical quantities, all of which clearly signal a first-order Mott transition. We thus obtain the phase diagram at zero temperature, where we find the coexistence region of the metal and the Mott insulator. We discuss how Hund's coupling affects the nature of the Mott transition in this system.
We study the Mott metal-insulator transition in the two-band Hubbard model with different hopping amplitudes t1 and t2 for the two orbitals on the two-dimensional square lattice by using non-magnetic variational wave functions, similarly to what has been considered in the limit of infinite dimensions by dynamical mean-field theory. We work out the phase diagram at half filling (i.e. two electrons per site) as a function of R = t2/t1 and the on-site Coulomb repulsion U, for two values of the Hund's coupling J = 0 and J/U = 0.1. Our results are in good agreement with previous dynamical mean-field theory calculations, demonstrating that the non-magnetic phase diagram is only slightly modified from infinite to two spatial dimensions. Three phases are present: a metallic one, for small values of U, where both orbitals are itinerant; a Mott insulator, for large values of U, where both orbitals are localized because of the Coulomb repulsion; and the so-called orbital-selective Mott insulator (OSMI), for small values of R and intermediate Us, where one orbital is localized while the other one is still itinerant. The effect of the Hund's coupling is two-fold: on one side, it favors the full Mott phase over the OSMI; on the other side, it stabilizes the OSMI at larger values of R.
Abstract Using the strong coupling diagram technique, we investigate the extended Hubbard model on a two-dimensional square lattice. This approach allows for charge and spin fluctuations and a short-range antiferromagnetic order at nonzero temperatures. The model features the first-order phase transition to states with alternating site occupations (SAO) at the intersite repulsion v = v c . In this work, we show that doping decreases v c . For a nonzero next-nearest neighbor hopping t ′ , less mobile carriers produce a stronger fall in v c . For half-filling and t ′ = 0 , we consider phase diagrams for a fixed temperature T, on-site U, and intersite repulsions. The diagrams contain regions of SAO, Mott insulator, and several metallic states distinguished by their densities of states. Two of them are characterized by a dip and a peak at the Fermi level. The dip originates from the Slater mechanism for itinerant electrons, while the peak to bound states of electrons with localized magnetic moments. The existence of these two metallic regions in the phase diagram is a manifestation of the Pomeranchuk effect. The boundary between these regions reveals itself as a kink in the curve v c (T) and as a maximum in the T dependence of the double occupancy D. Our calculated D for different values of v, U, and T are in semiquantitative agreement with Monte Carlo results.
Abstract We study the ground state of the three-band degenerate Hubbard model on a square lattice at integer fillings using the variational slave-spin mean field method. At half-filling, the method reproduces the well known result that the ground state is antiferromagnetic (AF) insulating at smaller values of Hubbard onsite repulsion U , while it becomes Mott insulating with Néel AF order at higher U . Away from half-filling, for two particles per site, we show that the model supports a ferromagnetic (FM) metallic state with fully polarized spins at sufficiently large U . The FM state occurs irrespective of the value of Hund’s coupling J . The ferromagnetism at J = 0 can be explained by the Stoner mechanism while that for J > 0 is shown to arise from the superexchange process. At this band filling, the Hund’s coupling J is known to have the Janus-faced effect on electronic correlations where it enhances correlations at smaller U while reducing it at higher U . We show that these two effects are separated by the paramagnetic (PM) to FM transition point. The former effect is obtained at the PM state while the latter occurs in the FM state. The FM phase also occurs for one particle per site but here Hund’s coupling J reduces the effect of electronic correlations at all U .
We present the influence of spin correlation on the metal-insulator transitions (MIT) in two-orbital Hubbard models by the Kotliar-Ruckenstein slave-boson approach. In the asymmetric half-filling situation, the two orbits simultaneously transit from conducting to insulating states with the increase of Coulomb correlation, accompanied by a paramagnetic (PM)-antiferromagnetic (AFM) transition. The orbital selective Mott transition found in the PM condition is completely suppressed over a wide correlation range, though it may exist in the systems away from half-filling. In the insulating state, the system crosses over from a partially-polarized spin-gapped phase in the intermediate correlation regime to an almost fully-polarized Mott insulating phase in the strong correlation regime. These results demonstrate that the spin modulation to the quasiparticle spectra brings much rich and more interesting MIT scenario in multi-orbital correlated systems.