arXiv subjects

Hiroki Nakai

Publications and source records attributed to Hiroki Nakai.

9 recordsLinked to original sources

arXiv2026

Quantum-geometry-driven exact ferromagnetic ground state in a nearly flat band

We construct a Hubbard model with a nearly flat band whose quantum geometry can be tuned independently of the energy dispersion and the Coulomb interaction. We show that, when the nearly flat band is half-filled, the exact ground state of the model exhibits ferromagnetism and that this ferromagnetism is stabilized by the quantum metric through the spin stiffness. Furthermore, we demonstrate that tuning the quantum geometry alone drives a magnetic phase transition. Our nonperturbative results without resorting to mean-field approximations reveal the quantum-geometric origin of ferromagnetism and the underlying many-body physics in dispersive-band systems.

cond-mat.str-el↗

arXiv2026

Quantum geometric ferromagnetism by singular saddle point

We propose ferromagnetism that occurs in electrons at a saddle point with band touching, which we call the singular saddle point. At the singular saddle point, the divergent quantum metric induces ferromagnetic correlation, and the logarithmic divergence of the density of states ensures ferromagnetism within Stoner theory. This is a prototypical example of quantum geometric ferromagnetism. The two-dimensional $t_{2g}$-orbital model accommodates the ferromagnetism by this mechanism, which is continuously connected to the exactly proven flat-band ferromagnetism.

cond-mat.str-el↗

arXiv2026

Spin-orbital exchange as a route to intertwined dipole-quadrupole orbital order in MnV$_2$O$_4$ under strong trigonal crystal field

Orbitally degenerate systems provide a promising platform for realizing novel quantum phases driven by spin-orbital exchange interactions, as described by the Kugel-Khomskii model. Spinel vanadates, in which orbital degrees of freedom remain active, exhibit structural and magnetic transitions accompanied by orbital ordering, but the nature of the orbital state in MnV$_2$O$_4$ remains under debate. Here, we combine first-principles calculations with an effective spin-orbital model to address this problem. We show that a significant trigonal crystal field is present in high-temperature cubic phase and plays an essential role in determining the low-energy degrees of freedom. Based on the resulting parameters, we construct an effective Hamiltonian beyond the conventional dominant-hopping approximation and demonstrate that subdominant hopping processes strongly modify the spin-orbital exchange interactions. As a result, the system stabilizes a two-in/two-out magnetic configuration featuring spin canting and intertwined dipole-quadrupole orbital order.

cond-mat.str-el↗

arXiv2025

Spin amplitude wave due to dipole-quadrupole hybridization in spin-1 pyrochlore magnets

We explore the quantum pseudospin-1 pyrochlore magnet featuring Fe$^{2+}$-based spinel oxides that addresses the formation of amplitude-modulated spin-density waves. We propose that the relatively small spin-orbit coupling and the small extra crystal field splitting in these materials create anisotropic exchange interactions and strong single-ion anisotropy, respectively, whose interplay becomes the source of quadrupolar moments selectively appearing on certain sublattices, leading to a spatially modulated hybrid of dipolar and quadrupolar moments. This mechanism represents the possibility of insulating magnets to form an exotic phase with coexisting liquid-solid properties.

cond-mat.str-el↗

arXiv2025

Spinor ice correlation in flat-band electronic states on kagome and pyrochlore lattices with spin-orbit coupling

We investigate the emergence and transformation of pinch-point singularities in the excitation spectrum of electronic flat band systems on kagome and pyrochlore lattices with spin-orbit coupling (SOC) and Coulomb interactions. While pinch points are widely recognized as signatures of classical spin liquids, they also appear in electronic flat-band systems when there exists a singular band-touching point to dispersive bands. We explore how SOC modifies the pinch-point structure in the chiral spin flat-band metallic state, which we term spinor-ice. The pinch point profile can rotate or redistribute its spectral weight, governed by a prefactor in the spectral function that primarily depends on the direction of the ground-state spin polarization, where we show that SOC flat bands could be experimentally probed by rotating the spin polarization of the injected electron to infer internal magnetic structures. These observations are discussed in conjunction with the angle-resolved photoemission spectroscopy (ARPES) and the application to the potential SOC flat-band material $\rm CsW_2O_6$. We also demonstrate the persistent residual pinch-point features under Coulomb interactions and deviations from the ideal flat-band limit.

cond-mat.str-el↗

arXiv2024

Pinch-point spectral singularity from the interference of topological loop states

Pinch point is a spectral discontinuity found in the neutron diffraction image of spin ice. Similar spectral singularity is commonly observed in a broad range of systems that have a close connection with flat bands. We focus on the electron flat band and its two topologically distinct classes of wavefunction: the compact localized state (CLS), and the non-contractible loop state (NLS). We establish their simple mathematical relationship, showing that different Bloch NLSs can be derived as momentum derivatives of a Bloch CLS, depending on the approaching direction toward the singular point. This CLS-NLS correspondence helps visualize the pinch point as an interference pattern among NLSs through a ``polarizer", which encodes the information about the location of singular momentum and the experimental techniques like spin-polarized photoemission spectroscopy. It helps extract topological information knit to microscopic electronic and magnetic structures.

cond-mat.mtrl-sci↗

arXiv2023

Deriving quantum spin model for a zigzag-chain ytterbium magnet with anisotropic exchange interactions

We derive a quantum spin Hamiltonian of the spin-1/2 zigzag chain realized in a rare earth ytterbium-based magnetic insulator, YbCuS2. This material undergoes a transition at 0.95K to an incommensurate magnetic phase with small moments, which does not conform to the nonmagnetic singlet ground state of the spin-1/2 Heisenberg model. We take account of octahedral crystal field effect, atomic spin-orbit coupling, and strong Coulomb interactions on Yb ions, and perform a four-order perturbation theory to evaluate the superexchange coupling constants. A small but finite anisotropic exchange coupling called Γ-term appears similarly to the case reported previously in other triangular-based magnets. By varying several material parameters, we figure out two important factors to enhance Γ-term. One is the splitting of excited f-states with two holes, which efficiently selects the perturbation terms associated with the lowest excited state having large total angular momentum, and accordingly with high spatial anisotropy. The other is the tilting of octahedra or distortion of S-Yb-S bond angle, which break the symmetry of the Slater-Koster overlap. These effects are systematically analyzed by the exchange anisotropy in units of pairs of octahedra within the local spin frame, which significantly reduces the complexity of directly referring to the Hamiltonian discussed in the global axis.

cond-mat.str-el↗

arXiv2022

Emergent chiral symmetry in non-bipartite kagome and pyrochlore lattices with spin-orbit coupling

Chiral symmetry in energy bands appears as perfectly symmetric anti-bonding and bonding pairs of energy levels. It has only been observed in a few classes of models with a bipartite lattice structure or Bogoliubov-de-Gennes systems having the pairwise basis. We show that the non-bipartite kagome and pyrochlore lattices can host chiral symmetric bands when the strong spin-orbit coupling is introduced. There, the electrons hop to their neighbors by always converting the spin orientation up-side-down, which allows the up and down spin bases to form fictitious bipartite connections. The gauge invariant Wilson loop operator defined on a triangular unit serves as a marker to detect the presence of chiral symmetry, and using this property, the chiral operator is constructed. This allows us to access their topological symmetry classes that can easily change with small perturbations.

cond-mat.str-el↗

arXiv2021

Perfect flat band with chirality and charge ordering out of strong spin-orbit interaction

Spin-orbit interaction established itself as a major role player for emergent phenomena in modern condensed matter including a topological insulator, spin liquid and spin-dependent transports. However, its function is rather limited to adding topological nature to each phases of matter. We prove by our spinor line graph theory that a very strong spin-orbit interaction realized in 5d pyrochlore electronic systems generates multiply degenerate perfect flat bands. Unlike any of the previous flat bands, the electrons living there localize in real space by destructively interfering with each other in a spin selective manner ruled by the SU(2) gauge field. These electrons avoid the Coulomb interaction by self-organizing their localized wave functions. This gives rise to the trimerized charge ordering hand in hand with a stiff spin chirality, which may explain the recently found exotic low-temperature insulating phase of CsW2O6.

cond-mat.str-el↗