arXiv subjects

Joji Nasu

Publications and source records attributed to Joji Nasu.

At least 19 recordsLinked to original sources

arXiv2026

Schwinger boson perturbation theory for spin-$S$ Kitaev-Heisenberg magnets: phase diagram and dynamical response near Kitaev spin liquids

We develop a Schwinger boson perturbative framework for the spin-$S$ Kitaev-Heisenberg model. The spin-liquid saddle point of the pure Kitaev model is used as the unperturbed state, and magnetic instabilities and dynamical spin correlations are evaluated around this saddle point. We decompose the Hamiltonian exactly into two parts by exploiting the Klein duality intrinsic to the Kitaev-Heisenberg model. We perform the random-phase approximation by taking the part invariant under the duality transformation as the unperturbed term and treating the remaining term, which changes sign under it, as the perturbation. We determine the phase boundaries separating the quantum spin-liquid regimes from the adjacent magnetically ordered phases for $S=1/2$, $1$, $3/2$, and $2$. The spin-liquid regions shrink rapidly with increasing $S$ and become very narrow at $S=2$. We also compute the spin dynamics of the spin-$S$ Kitaev-Heisenberg model, focusing on $S=1$, and find that the dressed dynamical spin structure factor retains a broad two-spinon continuum at finite energies, while the low-energy spectral weight softens at the ordering wave vectors of the adjacent magnetic phases. Our framework thus enables thermodynamic-limit calculations of spin dynamics near magnetic instabilities.

cond-mat.str-el↗

arXiv2026

Chiral bosonic mean-field Ansatz and spin dynamics in spin-1 Kitaev magnets

The Kitaev model is a paradigmatic system for realizing quantum spin liquids, but its higher-spin extensions are not exactly solvable, and their spin dynamics is less well understood than in the spin-1/2 case. In this work, we reexamine a previously introduced triplet-pairing $\phi_t = \pi/2$ phase pattern for the antiferromagnetic $S = 1$ Kitaev model and extend the analysis to weak symmetric off-diagonal exchanges $\Gamma$ and $\Gamma'$. Using a bond-operator formulation of Schwinger-boson mean-field theory, we calculate the dynamical spin structure factor for the triplet 0-flux and triplet $\pi/2$-flux Ans\"atze with a spin-correlation scheme appropriate for Kitaev interactions. In the pure Kitaev limit, the $\pi/2$-flux Ansatz yields a flatter spectrum than the 0-flux Ansatz. The real-space spin correlations show that the $\pi/2$-flux Ansatz suppresses longer-distance correlations more strongly than the 0-flux Ansatz, yielding a correlation pattern closer to the short-ranged form expected in the Kitaev limit. This comparison shows that the flatness of $S(\boldsymbol{q}, \omega)$ is tied to short-ranged spin correlations and is therefore an important consistency check, although it is not, by itself, a diagnostic of time-reversal-symmetry breaking. We then study weak off-diagonal exchanges along $\Gamma' = \Gamma$ near the pure Kitaev limit, taking the same-sign relation from analyses of candidate spin-1 Kitaev materials. Gapped solutions are obtained within the constrained $\pi/2$-flux manifold, and the spectra share the qualitative energy- and momentum-space features found by finite-size exact diagonalization. Taken together, these results support the triplet $\pi/2$-flux chiral bosonic Ansatz as a useful mean-field description of spin dynamics near the antiferromagnetic $S = 1$ Kitaev limit with weak off-diagonal exchanges.

cond-mat.str-el↗

arXiv2026

Halogen control of magnetic competition in Kitaev candidate Ru$X_3$ ($X =$ Cl, Br)

The spin-orbital Mott insulators Ru$X_3$ ($X =$ Cl, Br) have attracted considerable attention as promising candidate materials for realizing a Kitaev spin liquid. In this study, we construct effective pseudospin models from multiorbital Hubbard models derived from first-principles calculations and investigate the magnetic states of RuCl$_3$ and RuBr$_3$. From the constructed effective models, we find that RuBr$_3$ has more extended Wannier orbitals and stronger interlayer exchange interactions than RuCl$_3$. These interactions enhance three-dimensional correlations, consistent with the stronger antiferromagnetic tendency experimentally inferred for RuBr$_3$. Orbital-dependent Coulomb anisotropy further reduces the energy difference between ferromagnetic and zigzag states. Our results clarify how halogen substitution controls magnetic competition in Ru$X_3$ through interlayer exchange interactions and effects of orbital-dependent Coulomb interactions.

cond-mat.str-el↗

arXiv2026

Dynamical spin correlations in kagome antiferromagnets: comparison of Abrikosov fermion and Schwinger boson approaches beyond mean field

Quantum spin liquids exhibit fractionalized spin excitations as a consequence of strong quantum many-body effects. The kagome antiferromagnetic Heisenberg model is a promising candidate for a quantum spin-liquid ground state; however, the nature of its excitation spectrum remains controversial, particularly regarding the presence of a spin gap and the gauge structure coupled to fractional quasiparticles. To address these issues, parton approaches have been extensively employed, where spin operators are represented in terms of fermionic or bosonic quasiparticles within the Abrikosov fermion and Schwinger boson frameworks. Thus far, these approaches have been pursued independently, and it has remained unclear how the results obtained from these frameworks compare, particularly with respect to the spin dynamics and gauge structure of the kagome antiferromagnet. Here, we investigate the dynamical spin structure factor of the antiferromagnetic Heisenberg model with a Dzyaloshinskii-Moriya interaction on the kagome lattice, relevant to herbertsmithite, by employing both approaches. We find that the dynamical spin structure factor obtained from the Abrikosov fermion mean-field theory exhibits dome-shaped features, and that its continuum structure significantly depends on the gauge structure of the spin-liquid ansatz. On the other hand, the Schwinger boson mean-field theory yields a concave-down structure in the low-energy region, distinct from that obtained using the Abrikosov fermion approach. Moreover, incorporating many-body effects beyond the mean-field approximation substantially reduces the low-energy gap and enhances the low-energy spectral weight, consistent with experimental observations. Our results suggest the importance of many-body effects in the Schwinger boson theory for capturing the low-energy spin dynamics of kagome antiferromagnets.

cond-mat.str-el↗

arXiv2026

Quantum signal processing in Hilbert space fragmented systems

Quantum signal processing (QSP), originally developed for composite pulse sequences in nuclear magnetic resonance systems, has recently attracted attention as a unified framework for quantum algorithms. A pioneering study applied QSP to nonequilibrium control in integrable many-body systems, enabling the realization of nonequilibrium dynamics with greater flexibility than Floquet engineering. However, extending QSP to nonintegrable systems faces fundamental obstacles arising from the limited number of conserved quantities and thermalization. In this work, we propose a protocol that leverages QSP in systems exhibiting Hilbert space fragmentation (HSF). Specifically, we consider a pair-hopping model with four-fold periodic potentials that exhibits an HSF structure, thereby providing integrable and nonintegrable sectors within a single system. We analytically show that nonequilibrium dynamics can be flexibly designed through QSP engineered by these potentials in the integrable sectors. In contrast, we numerically identify signatures of thermalization in the nonintegrable sectors. Remarkably, by inserting domain walls, we achieve parallel control of multiple quantum dynamics within a single system. This approach sheds light on the control of nonequilibrium dynamics from the perspective of quantum computation by extending the scope of QSP to nonintegrable systems.

quant-ph↗

arXiv2026

Formulation of intrinsic nonlinear thermal conductivity for bosonic systems using quantum kinetic equation

Nonlinear responses in transport phenomena have attracted significant attention because they can arise even when linear responses are forbidden by symmetry, with the quantum geometry of Bloch wave functions playing an essential role. While such effects have been extensively studied in electric transport, similar quantum-geometric mechanisms are also expected to govern nonlinear thermal transport. In particular, thermal responses are crucial in bosonic systems such as magnons and phonons, which are charge-neutral quasiparticles. However, a consistent theoretical description of nonlinear thermal transport remains challenging because of the difficulty in the treatment of energy magnetization in higher-order responses with Luttinger's gravitational potential method. Here, we formulate the intrinsic nonlinear thermal conductivity of bosonic systems using a quantum kinetic equation approach that avoids Luttinger's method and naturally incorporates contributions from energy magnetization. We identify three distinct contributions to the nonlinear thermal conductivity: two expressed in terms of quantum-geometric quantities, namely the quantum metric and the thermal Berry-connection polarizability (TBCP), and a third determined solely by the band dispersions. Applying our formalism to a specific quantum spin model within linear spin-wave theory, we show that the TBCP term dominates the nonlinear thermal Hall effect in the absence of threefold symmetry. Our results differ quantitatively from those obtained using semiclassical theory, thereby highlighting the importance of quantum corrections beyond the semiclassical picture. These findings establish a general framework for intrinsic nonlinear thermal responses in bosonic systems and reveal quantum-geometric mechanisms underlying thermal transport beyond linear response theory.

cond-mat.str-el↗

arXiv2025

Schwinger boson theory for $S=1$ Kitaev quantum spin liquids

The Kitaev model is an exactly solvable model with a quantum spin liquid ground state. While this model was originally proposed as an $S=1/2$ spin model on a honeycomb lattice, extensions to higher-spin systems have recently attracted attention. In contrast to the $S=1/2$ case, such higher-$S$ models are not exactly solvable and remain poorly understood, particularly for spin excitations at finite temperatures. Here, we focus on the $S=1$ Kitaev model, which is proposed to host bosonic quasiparticles. We investigate this model using Schwinger boson mean-field theory, introducing bosonic spinons as fractional quasiparticles by extending bond operators to address anisotropic spin interactions. We determine the mean-field parameters that realize a quantum spin liquid in both ferromagnetic and antiferromagnetic Kitaev models. Based on this ansatz, we calculate dynamical and equal-time spin structure factors. We find that the conventional scheme based on Wick decoupling with respect to spinons to calculate spin correlations, the resultant spin structure factors exhibit a momentum dependence that is not consistent with the sign structure expected from the exchange interaction. To resolve this issue, we propose an alternative evaluation based on decoupling with respect to bond operators. We demonstrate that, in our scheme, this discrepancy is removed, and the momentum dependence of the spin structure factors is consistent with the sign of the exchange constant. We also compute the temperature evolution of the dynamical spin structure factor and find that the zero-temperature continuum splits into two distinct structures as temperature increases, which can be understood in terms of the bandwidth narrowing of spinons. Finally, we clarify why the two decoupling schemes result in different momentum dependences and discuss their relationship to previous studies.

cond-mat.str-el↗

arXiv2025

Thermal Hall transport in Kitaev spin liquids

We investigate the thermal Hall conductivity in the Kitaev model with additional interactions under a magnetic field, employing a finite-temperature tensor network method benchmarked by a thermal pure quantum state technique. We find that the thermal Hall conductivity divided by temperature, $\kappa_{xy}/T$, significantly overshoots the value of the half-integer quantization and exhibits a pronounced hump while decreasing temperature. Moreover, we show that the field-direction dependence of $\kappa_{xy}/T$ is consistent with the sign of the Chern number associated with the Majorana fermions across a wide range of magnetic fields. We also demonstrate that the additional off-diagonal interactions, known as the $\Gamma$ and $\Gamma^{\prime}$ terms, considerably affect $\kappa_{xy}/T$. In particular, we show that positive $\Gamma$ and negative $\Gamma^{\prime}$ lead to a remarkable enhancement in the intermediate temperature region. From the comparison with the classical counterpart, we reveal that the effects of the $\Gamma$ term go beyond the classical picture, indicating significant quantum fluctuation effects, while those of the $\Gamma^\prime$ term are well captured at the classical level. These comprehensive analyses indicate that the enhanced thermal Hall response is consistently explained by dominant contributions from topological Majorana fermions, even within the polarized regime beyond the critical field. Our approach not only establishes a robust theoretical framework for understanding the thermal Hall transport in Kitaev materials such as $\alpha$-RuCl$_{3}$, but also offers a promising pathway to bridge the gap between theories and experiments across a wide range of strongly correlated materials.

cond-mat.str-el↗

arXiv2025

Formulation of spin Nernst effect for spin-nonconserving insulating magnets

The spin Nernst effect, an antisymmetric response of a spin current to a temperature gradient, has attracted attention as spin transport phenomenon arising from the topologically nontrivial band structure of carriers. This effect can occur not only in itinerant electron systems but also in localized electron systems that emerge due to electronic correlations. In such systems, elementary excitations behaving as bosons govern spin transport, and magnetic interactions originating from spin-orbit coupling can induce a topologically nontrivial band structure. However, such magnetic interactions can potentially break spin conservation, thereby preventing conventional spin currents from being conserved. In this study, starting from a general localized electron model, we formulate the spin Nernst effect in terms of a conserved spin current that remains applicable even in spin-nonconserving systems. To address the torque term appearing in the conserved spin current, we adopt semiclassical theory and derive an expression for the spin Nernst coefficient for bosonic systems. This coefficient consists of two terms originating from the Berry curvature and the quantum metric, which are distinctly different from the spin Berry curvature obtained in an approach that neglects the torque term. We apply our framework to two specific quantum spin models, the Kitaev-Heisenberg and Shastry-Sutherland models, and calculate the temperature dependence of the spin Nernst coefficient. We find that this quantity significantly differs from that obtained by neglecting the torque term in both models. Furthermore, we clarify that the impact of the torque term on the spin Nernst effect strongly depends on the model parameters, suggesting that our formulation based on the conserved spin current is essential for understanding this effect in insulating magnets.

cond-mat.str-el↗

arXiv2025

Magnetic-field effect on excitonic condensation emergent in extended Falicov-Kimball model

We investigate the effects of magnetic fields on excitonic condensation in the extended Falicov-Kimball model, which is a spinless two-orbital Hubbard model with orbital splitting. In lattice systems under magnetic fields up to several tens of teslas, Zeeman effects on electron spins have been extensively studied, while the impact on orbital motion has often been considered negligible. However, the recent capability to generate ultra-high magnetic fields exceeding 1000 T has renewed interest in understanding their influence on ordered phases in correlated electron systems, beyond spin-related phenomena. To examine these effects, we incorporate a magnetic field into the extended Falicov-Kimball model by introducing the Peierls phase into the transfer integrals, enabling the study of orbital motion. Using the Hartree-Fock approximation, we reveal a nonmonotonic response of the excitonic order parameter to increasing magnetic fields. At sufficiently high fields, the excitonic order is suppressed, resulting in a disordered insulating state characterized by partial occupation of the two orbitals with nonzero Chern numbers. This state is distinct from a fully orbital-polarized configuration. Furthermore, our analysis of an excitonic supersolid phase, in which excitonic and orbital orders coexist, demonstrates that orbital order remains robust under magnetic fields, while excitonic condensation is suppressed. These findings provide insights into the interplay between orbital motion and magnetic fields in multi-orbital correlated electron systems.

cond-mat.str-el↗

arXiv2024

Controlling discrete time crystals via single-site operations in zero-field diamond quantum simulators

Discrete time crystals (DTCs) have emerged as novel nonequilibrium phases of matter that spontaneously break discrete time-translation symmetry in periodically driven systems. Rigorous experimental validation of DTCs, which requires highly controllable quantum simulators, has stimulated extensive research across diverse fields in condensed matter physics and quantum information technologies. Among these advances, DTCs were demonstrated in a hybrid spin register within diamond, comprising a processor spin and surrounding memory spins. However, in conventional strategies involving a bias magnetic field, the field application effectively restricts the controllability of the processor spin. This limitation can be a significant barrier to the next goal of DTCs: achieving multifunctionality through enhanced local controllability. In this study, we theoretically propose multiple DTC protocols through the design of specific single-site control within the entire system. To this end, we consider a concrete model of a diamond-based quantum simulator operating without a bias magnetic field, thereby eliminating the restrictions on the processor spin. Our findings demonstrate that single-site operations enable access to DTCs with multiple distinct features in terms of periodicity and lifetime. Therefore, this approach provides a promising platform for creating diverse DTCs induced by single-site operations.

cond-mat.stat-mech↗

arXiv2024

Nonlocal correlations in quantum energy teleportation: perspectives from their Majorana representations and information thermodynamics

Motivated by anomalous nonlocal correlation in the Kitaev spin liquids, we propose a quantum energy teleportation protocol between remote partners Alice and Bob on a quantum spin model, and examine how its performance is characterized by Majorana fermions that clearly depict nonlocal correlations inherent in the model. In our model, Bob's energy extraction is activated by local energy injection by Alice's projective measurement and subsequent classical communication of the measurement result. We derive two formulae: one for the maximally extracted energy by the protocol and the other for the maximum of energy reduction at Bob's local site. We find that the extracted energy becomes positive when a nonlocal correlator defined by Majorana fermions at Alice's and Bob's sites is finite. We also find that the amount of the energy reduction becomes positive when another nonlocal Majorana correlator is finite. In both formulae, the correlators appear as a result of Bob's feedback unitary operation. We discuss effective information-thermodynamical aspects behind the protocol at zero temperature.

quant-ph↗

arXiv2024

Impact of triplon damping on thermal Hall conductivity in Shastry-Sutherland model

We investigate the thermal Hall effect in the Shastry-Sutherland model, incorporating interactions between quasiparticle excitations. In this model, with strong nearest-neighbor interactions, the ground state is well described by the direct product of spin-singlet states, and the elementary excitations to spin-triplet states are known as triplons. In candidate materials for this model, Dzyaloshinskii-Moriya interactions are inevitably present, resulting in topologically non-trivial band structures for triplon excitations. In this study, we examine quasiparticle damping due to triplon-triplon interactions as a potential factor contributing to the suppression of the thermal Hall effect. We apply nonlinear flavor-wave theory to the Shastry-Sutherland model and treat triplons as bosonic excitations. We calculate the triplon damping rate using the imaginary Dyson equation approach and evaluate the thermal Hall conductivity. Our findings demonstrate that triplons with nonzero Berry curvature are scattered by thermally excited triplons. This scattering effect suppresses the thermal Hall conductivity, particularly at finite temperatures, highlighting the significant role of triplon damping in the thermal Hall effect.

cond-mat.str-el↗

arXiv2024

Real-time control of non-Abelian anyons in Kitaev spin liquid under energy dissipation

Quantum spin liquids realized in the Kitaev model offer a platform for fractionalization of spin into two quasiparticles: itinerant Majoranas and localized visons. Introducing a uniform weak magnetic field associates a Majorana zero mode with each vison excitation. The vison accompanied by a Majorana zero mode is known to behave as a non-Abelian anyon, which has garnered significant attention for its potential applications in topological quantum computing. Although spatial and temporal control of these anyons is essential for exploring their applicability in quantum computing, numerical simulations of creating, moving, and annihilating anyons by an external field remain challenging as this field violates the exact solvability of the Kitaev model. Moreover, such a field to control anyons may disturb the quantum state due to the energy injection it causes. In this study, by introducing energy dissipation phenomenologically in real-time simulations, we demonstrate that the generation, movement, and annihilation of vison excitations can be achieved while maintaining their localization. We find that a vison can be moved in a desired direction by using time-dependent local magnetic fields or gradient fields, and it remains accompanied by a Majorana zero mode even after its movement. We also reveal that a larger spatial extent of the Majorana zero modes bound to a vison facilitates the movement of the vison with smaller field gradients. Furthermore, our numerical simulations demonstrate pair creation and annihilation of visons, triggered by time-dependent magnetic fields. The results obtained in this study highlight the significance of energy dissipation in controlling non-Abelian anyons, which will stimulate further investigations into the nonequilibrium dynamics of fractional quasiparticles in strongly correlated electron systems, as well as studies for applications in quantum computation.

cond-mat.str-el↗

arXiv2024

A review on magnetic field induced spin crossover in LaCoO$_{3}$ up to 600 T

\lco{} is known for its two-step spin crossover as a function of temperature. Despite efforts spanning over half a century, the origin of this phenomenon is still debated, particularly regarding how the microscopic spin states are involved in the observed macroscopic two-step spin crossover. High magnetic field studies on LaCoO$_{3}$ are performed because the magnetic field-induced spin crossover is induced, where the magnetic excited states become more stable in high magnetic fields than the non-magnetic ground states. This review focuses on the findings in LaCoO$_{3}$ at high magnetic fields over the last decade. A complex phase diagram has been revealed at high magnetic fields instead of solving the conventional problem of LaCoO$_{3}$. It suggests that appreciable spin state correlations are in play in LaCoO$_{3}$. The possibility of exciton condensation is also discussed.

cond-mat.str-el↗

arXiv2024

Thermal Hall effect incorporating magnon damping in localized spin systems

We propose a theory for thermal Hall transport mediated by magnons to address the impact of their damping resulting from magnon-magnon interactions in insulating magnets. This phenomenon is anticipated to be particularly significant in systems characterized by strong quantum fluctuations, exemplified by spin-1/2 systems. Employing a nonlinear flavor-wave theory, we analyze a general model for localized electron systems and develop a formulation for thermal conductivity based on a perturbation theory, utilizing bosonic Green's functions with a nonzero self-energy. We derive the expression of the thermal Hall conductivity incorporating magnon damping. To demonstrate the applicability of the obtained representation, we adopt it to two $S=1/2$ quantum spin models on a honeycomb lattice. In calculations for these systems, we make use of the self-consistent imaginary Dyson equation approach at finite temperatures for evaluating the magnon damping rate. In both systems, the thermal Hall conductivity is diminished due to the introduction of magnon damping over a wide temperature range. This effect arises due to the smearing of magnon spectra with nonzero Berry curvatures. We also discuss the relation to the damping of chiral edge modes of magnons. Our formulation can be applied to various localized electron systems as we begin with a general Hamiltonian for these systems. Our findings shed light on a new aspect of topological magnonics emergent from many-body effects and will stimulate further investigations on the impact of magnon damping on topological phenomena.

cond-mat.str-el↗

arXiv2024

Spin Seebeck Effect as a Probe for Majorana Fermions in Kitaev Spin Liquids

Quantum entanglement in strongly correlated electron systems often leads to exotic elementary excitations. Quantum spin liquids (QSLs) provide a paradigmatic example, where the elementary excitations are described by fractional quasiparticles such as spinons. However, such fractional quasiparticles behave differently from electrons, making their experimental identification challenging. Here, we theoretically investigate the spin Seebeck effect, which is a thermoelectric response via a spin current, as an efficient probe of the fractional quasiparticles in QSLs, focusing on the Kitaev honeycomb model. By comprehensive studies using the real-time dynamics, the perturbation theory, and the linear spin-wave theory based on the tunnel spin-current theory, we find that the spin current is induced by thermal gradient in the Kitaev spin liquid, via the low-energy fractional Majorana excitations. This underscores the ability of Majorana fermions to carry spin current, despite lacking spin angular momentum. Furthermore, we find that the induced spin current changes its sign depending on the sign of the Kitaev interaction, indicating that the Majorana fermions contribute to the spin current with (up-)down-spin like nature when the exchange coupling is (anti)ferromagnetic. Thus, in contrast to the negative spin current already found in a one-dimensional QSL, our finding reveals that the spin Seebeck effect can exhibit either positive or negative signals, contingent upon the nature of fractional excitations in the QSLs. We also clarify contrasting field-angle dependence between the Kitaev spin liquid in the low-field limit and the high-field ferromagnetic state, which is useful for the experimental identification. Our finding suggests that the spin Seebeck effect could be used not only to detect fractional quasiparticles emerging in QSLs but also to generate and control them.

cond-mat.str-el↗

arXiv2023

Effects of magnetic fields and orbital angular momentum on excitonic condensation in two-orbital Hubbard model

We investigate the magnetic-field effects on a two-orbital Hubbard model that describes multiple spin states. Cobalt oxides have been investigated as materials possessing spin-state degrees of freedom due to the interplay between the Hund coupling interaction and crystalline field effect. In the competing region, quantum hybridizations between distinct spin states are expected to emerge, corresponding to excitonic condensation. Applied magnetic fields could also induce such a competition. To understand magnetic-field effects on excitonic condensation in multi-orbital systems, it is crucial to account for contributions from both spin and orbital degrees of freedom to magnetic properties. Here, we study field-induced phenomena in the two-orbital Hubbard model by focusing on the role of the orbital angular momentum. We comprehensively analyze this model on a square lattice employing the Hartree-Fock approximation. Omitting contributions from the orbital moment, we find that an applied magnetic field gives rise to two excitonic phases, besides the spin-state ordered phase, between the nonmagnetic low-spin and spin-polarized high-spin phases. One of these excitonic phases manifests a staggered-type spin-state order, interpreted as an excitonic supersolid state. Conversely, the other phase is not accompanied by it and exhibits only a spin polarization due to the applied magnetic field. When spin-orbit coupling is present, this phase displays a ferrimagnetic spin alignment attributed to spin anisotropy. Our analysis also reveals that incorporating the contribution of the orbital magnetic moment to the Zeeman term significantly alters the overall structure of the phase diagram. Notably, the orbital magnetization destabilizes the excitonic phase in contrast to scenarios without this contribution. We also discuss the relevance of our findings to real materials, such as cobalt oxides.

cond-mat.str-el↗