菅 誠一郎

We investigate ground state energies and low-energy excitations of the S = 1/2 Kitaev-Heisenberg model on honeycomb lattices by using dimer series expansions. We find that dimer series expansions can approach the close vicinity of the Kitaev limit, where the Heisenberg interaction is absent, in the lower order expansion than the Ising series expansion. When the system approaches the Kitaev limit, low-lying modes in the zigzag and Neel phases become flatter except for the Bragg wave numbers.

Contrary to the original expectation, Na$_2$IrO$_3$ is not a Kitaev's quantum spin liquid (QSL) but shows a zig-zag-type antiferromagnetic order in experiments. Here we propose experimental clues and criteria to measure how a material in hand is close to the Kitaev's QSL state. For this purpose, we systematically study thermal and spin excitations of a generalized Kitaev-Heisenberg model studied by Chaloupka $et$ $al$. in Phys. Rev. Lett. 110, 097204 (2013) and an effective ab initio Hamiltonian for Na$_2$IrO$_3$ proposed by Yamaji $et$ $al$. in Phys. Rev. Lett. 113, 107201 (2014), by employing a numerical diagonalization method. We reveal that closeness to the Kitaev's QSL is characterized by the following properties, besides trivial criteria such as reduction of magnetic ordered moments and Neel temperatures: (1) Two peaks in the temperature dependence of specific heat at $T_{\ell}$ and $T_h$ caused by the fractionalization of spin to two types of Majorana fermions. (2) In between the double peak, prominent plateau or shoulder pinned at $(R/2)\ln 2$ in the temperature dependence of entropy, where $R$ is the gas constant. (3) Failure of the linear spin wave approximation at the low-lying excitations of dynamical structure factors. (4) Small ratio $T_{\ell}/T_h$ close to or less than 0.03. According to the proposed criteria, Na$_2$IrO$_3$ is categorized to a compound close to the Kitaev's QSL, and is proven to be a promising candidate for the realization of the QSL if the relevant material parameters can further be tuned by making thin film of Na$_2$IrO$_3$ on various substrates or applying axial pressure perpendicular to the honeycomb networks of iridium ions. Applications of these characterization to (Na$_{1-x}$Li$_x$)$_2$IrO$_3$ and other related materials are also discussed.

We investigate the dynamical properties of Na2IrO3. For five effective models proposed for Na2IrO3, we numerically calculate dynamical structure factors (DSFs) with an exact diagonalization method. An effective model obtained from ab initio calculations explains inelastic neutron scattering experiments adequately. We further calculate excitation modes based on linearized spin-wave theory. The spin-wave excitation of the effective models obtained by ab initio calculations disagrees with the low-lying excitation of DSFs. We attribute this discrepancy to the location of Na2IrO3 in a parameter space close to the phase boundary with the Kitaev spin-liquid phase.

We investigate the dynamical properties of Na2IrO3. For five effective models proposed for Na2IrO3, we numerically calculate dynamical structure factors (DSFs) with an exact diagonalization method. An effective model obtained from ab initio calculations explains inelastic neutron scattering experiments adequately. We further calculate excitation modes based on linearized spin-wave theory. The spin-wave excitation of the effective models obtained by ab initio calculations disagrees with the low-lying excitation of DSFs. We attribute this discrepancy to the location of Na2IrO3 in a parameter space close to the phase boundary with the Kitaev spin-liquid phase.

We investigate the pairing symmetry of the superfluid state in repulsively interacting three-component (color) fermionic atoms in optical lattices. When two of the three color-dependent repulsions are much stronger than the other, pairing symmetry is an extended s wave, although the superfluid state appears adjacent to the paired Mott insulator in the phase diagram. On the other hand, when two of the three color-dependent repulsions are weaker than the other, pairing symmetry is a d(x2-y2) wave. This change in pairing symmetry is attributed to the change in the dominant quantum fluctuations from the density fluctuations of unpaired atoms and the color-density wave fluctuations to the color-selective antiferromagnet fluctuations. This phenomenon can be studied using existing experimental techniques.

We investigate the effects of a repulsive three-body interaction on the Mott transition of the repulsively interacting three-component fermionic atoms in optical lattices by means of the self-energy functional approach. We find that the three-body repulsion hardly affects the qualitative features of the Mott transition, because the three-body repulsion does not compete with the two-body repulsions. When the three-body repulsion is extremely strong, the triple occupancy vanishes in the Fermi liquid state. This situation is equivalent to that caused by strong three-body losses. Our results imply that three-body losses have little influence on the Mott transitions in the repulsively interacting three-component fermionic atoms in optical lattices.

We review our theoretical analysis of repulsively interacting three-component fermionic atoms in optical lattices. We discuss quantum phase transitions at around half filling with a balanced population by focusing on Mott transitions, staggered ordering, and superfluidity. At half filling (with 3/2 atoms per site), characteristic Mott transitions are induced by the anisotropic interactions, where two-particle repulsions between any two of the three colors have different strengths. At half filling, two types of staggered ordered states appear at low temperatures depending on the anisotropy of the interactions. As the temperature increases, phase transitions occur from the staggered ordered states to the unordered Mott states. Deviating from half filling, an exotic superfluid state appears close to a regime in which the Mott transition occurs. We explain the origin of these phase transitions and present the finite-temperature phase diagrams. © 2013 World Scientific Publishing Company.

We investigate the superfluid state of repulsively interacting three-component (color) fermionic atoms in optical lattices. When the anisotropy of the three repulsive interactions is strong, atoms of two of the three colors form Cooper pairs and atoms of the third color remain a Fermi liquid. An effective attractive interaction is induced by density fluctuations of the third-color atoms. This superfluid state is stable against changes in filling close to half filling. We determine the phase diagrams in terms of temperature, filling, and the anisotropy of the repulsive interactions.

We develop a perturbative approach combined with the dynamical mean-field theory for investigating the Mott transition in repulsively interacting three-component fermionic atoms in optical lattices. We show that this method captures the essentials of the correlation effects and describes well the crossover between the Fermi liquid and the paired Mott insulator.

We investigate the finite-temperature properties of attractive three-component (colors) fermionic atoms in optical lattices using a self-energy functional approach. As the strength of the attractive interaction increases in the low temperature region, a second-order transition occurs from a Fermi liquid to a color superfluid (CSF). In the strong attractive region, a first-order transition occurs from a CSF to a trionic state. In the high temperature region, a cross-over between a Fermi liquid and a trionic state is observed with increasing the strength of the attractive interaction. The cross-over region for fixed temperature is almost independent of filling.

We study the Kondo effect of a two-orbital vertical quantum dot (QD) coupled to two ferromagnetic leads by employing an equation of motion method. When the ferromagnetic leads are coupled with parallel spin polarization, we find three peaks in the single-particle excitation spectra. The middle one is the Kondo resonance caused by the orbital degrees of freedom. In magnetic fields, the Kondo effect vanishes. However, at a certain magnetic field new twofold degenerate states arise and the Kondo effect emerges there. In contrast, when the ferromagnetic leads are coupled with antiparallel spin polarization, the Kondo effect caused by the spin (orbital) degrees of freedom survives (is suppressed) in magnetic fields. We investigate the field dependence of the conductance in the parallel and antiparallel spin polarizations of the leads and find that the conductance changes noticeably in magnetic fields.

We investigate three-component (colors) fermionic atoms with anisotropic attractive interactions in optical lattices at half filling using the dynamical mean field theory. In the weakly interacting region the color superfluid (CSF) state emerges, where atoms with two of three colors form the Cooper pairs. As the interaction is increased, a first-order quantum phase transition to the trionic state occurs, where singlet bound states of three different color atoms are formed. We show that the trionic state survives up to a fairly large anisotropic region. The phase diagram for the CSF and trionic states is obtained.

We investigate finite-temperature properties of three-component (color) repulsive fermionic atoms in optical lattices at half filling using a self-energy functional approach. For a certain anisotropy of the interactions, we find a color density-wave (DW) state at low temperatures. In the weakly interacting region, the second-order phase transition from the color DW state to the Fermi-liquid state occurs with increasing temperature. In the strongly interacting region, by contrast, the first-order transition from the color DW state to a color selective Mott transition (CSMT) state or a Mott insulating state occurs. As the interaction increases above the critical temperatures, we observe a crossover from the CSMT state to the Mott insulating state.

We investigate quantum phase transitions of three-component (colors) repulsive fermionic atoms in optical lattices, using dynamical mean field theory. For the isotropic interaction system, a Mott transition occurs at commensurate 1/3 and 2/3 fillings, while the system remains a Fermi liquid at incommensurate other filling. For the anisotropic interaction system, we find that at half-filling there occur a color-selective Mott transition and a color superfluid transition driven by the repulsive interaction. (C) 2009 Elsevier B.V. All rights reserved.

We investigate the Mott transitions of three-component (colors) repulsive fermionic atoms in optical lattices using the dynamical mean-field theory. We find that for SU(3) symmetry-breaking interactions, the Mott transition occurs at incommensurate half filling. As a result, a characteristic Mott insulating state appears, where paired atoms with two different colors and atoms with the third color are localized, and either of these states is randomly distributed in each site. We also find another Mott state, where atoms with two different colors are randomly localized at different sites, and atoms with the third color remain itinerant. We demonstrate that double occupancy measurements show characteristics of these exotic Mott phases.

We investigate the Kondo effect of a multiorbital quantum dot coupled to ferromagnetic leads, using an equation of motion method. It is shown that the Kondo peak splits into three peaks and the middle one is located close to the Fermi energy. As the spin polarization of the leads is increased, the splitting between the highest and lowest energy peaks increases. The results indicate that the Kondo effect caused by the orbital degrees of freedom remains, while the Kondo effect caused by the spin degrees of freedom is suppressed. The origin of the suppressed spin Kondo effect is discussed in terms of the renormalized energy level of the quantum dot. (C) 2009 Elsevier B.V. All rights reserved.

We investigate three-component (colors) repulsive fermionic atoms in optical lattices using the dynamical mean-field theory. Depending on the anisotropy of the repulsive interactions, either a color density-wave state or a color-selective staggered state appears at half filling. In the former state, pairs of atoms with two of the three colors and atoms with the third color occupy different sites alternately. In the latter state, atoms with two of the three colors occupy different sites alternately and atoms with the third color are itinerant throughout the system. When the interactions are isotropic, both states are degenerate. We discuss the results using an effective model.

We study spin and orbital correlations in the two-orbital Hubbard model with the different bandwidths at quarter filling by means of the cellular dynamical mean field theory combined with the noncrossing approximation. We demonstrate that the ferromagnetic-antiferro-orbital insulating state is stabilized in the system with the same bandwidth and the antiferromagnetic-ferro-orbital insulating state appears when the difference of the bandwidth is quite large. In the intermediate region, we find that the competition between the two states occurs and this competition gives rise to the heavy Fermi-liquid metallic state.

We study spin and orbital correlations in the two-orbital Hubbard model with different bandwidths at quarter filling by means of the cellular dynamical mean field theory combined with the noncrossing approximation. We show that the ferromagnetic-antiferro-orbital insulating state is stabilized by the Hund's coupling in the system with the same bandwidths and the antiferromagnetic-ferro-orbital insulating state appears when the difference of bandwidths is quite large. We find that the competition between the two states occurs in the intermediate region and this competition gives rise to the strongly renormalized metallic state.

We investigate the finite-temperature properties of attractive three-component (colors) fermionic atoms in optical lattices using a self-energy functional approach. As the strength of the attractive interaction increases in the low-temperature region, we observe a second-order transition from a Fermi liquid to a color superfluid (CSF), where atoms from two of the three colors form Cooper pairs. In the strong attractive region, we observe a first-order transition from a CSF to a trionic state, where three atoms with different colors form singlet bound states. A crossover between a Fermi liquid and a trionic state is observed in the high-temperature region. We present a phase diagram covering zero to finite temperatures. We demonstrate that the CSF transition temperature is enhanced by the anisotropy of the attractive interaction.

We investigate the temperature region in which a Tomonaga-Luttinger liquid (TLL) description of the charge sector of the one-dimensional Hubbard model is valid. By using the thermodynamic Bethe ansatz method, electron number is calculated at finite temperatures and fixed chemical potential. We observe maximum electron number as a function of temperature close to the chemical potential of the upper critical value that corresponds to half filling. As the chemical potential approaches the upper critical value from below, the temperature (T-M) at which the electron number shows its maximum asymptotically approaches a universal relation. We show that, below the energy corresponding to T-M, the charge excitation spectrum nearly obeys a linear dispersion relation. The results demonstrate that T-M marks the important temperature below which TLL is realized.

We investigate the quasiparticle dynamics in the two-orbital Hubbard model on the square lattice at quarter filling by means of the cellular dynamical mean-field theory. We show that the Fermi-liquid state is stabilized up to the large Hubbard interactions in the symmetric case without Hund's coupling, and find the heavy quasiparticles around the metal-insulator boundary. It is elucidated that Hund's coupling enhances the antiferro-orbital correlations, which give rise to the pseudogap behavior in the single-particle excitations. We also find the nonmonotonic temperature dependence in the quasiparticle dynamics for intermediate strength of Hund's coupling, and clarify that it is caused by the competition between the Fermi-liquid formation and the antiferro-orbital fluctuations. © 2009 The American Physical Society.

We investigate the quasiparticle dynamics in the two-orbital Hubbard model on the square lattice at quarter filling by means of the cellular dynamical mean-field theory. We show that the Fermi-liquid state is stabilized up to the large Hubbard interactions in the symmetric case without Hund's coupling, and find the heavy quasiparticles around the metal-insulator boundary. It is elucidated that Hund's coupling enhances the antiferro-orbital correlations, which give rise to the pseudogap behavior in the single-particle excitations. We also find the nonmonotonic temperature dependence in the quasiparticle dynamics for intermediate strength of Hund's coupling, and clarify that it is caused by the competition between the Fermi-liquid formation and the antiferro-orbital fluctuations.

We study two-band effects on ultracold fermionic atoms in optical lattices by means of dynamical mean-field theory. We find that at half filling an atomic-density-wave (ADW) state emerges owing to the two-band effects in the attractive interaction region, while an antiferromagnetic state appears in the repulsive interaction region. As the orbital splitting is increased, quantum phase transitions from the ADW state to the superfluid state and from the antiferromagnetic state to the metallic state occur in the corresponding regions. By systematically changing the orbital splitting and the interaction, we obtain the phase diagram at half filling. The results are discussed using the effective boson model derived for strong attractive interaction. © 2009 The American Physical Society.

We study two-band effects on ultracold fermionic atoms in optical lattices by means of dynamical mean-field theory. We find that at half filling an atomic-density-wave (ADW) state emerges owing to the two-band effects in the attractive interaction region, while an antiferromagnetic state appears in the repulsive interaction region. As the orbital splitting is increased, quantum phase transitions from the ADW state to the superfluid state and from the antiferromagnetic state to the metallic state occur in the corresponding regions. By systematically changing the orbital splitting and the interaction, we obtain the phase diagram at half filling. The results are discussed using the effective boson model derived for strong attractive interaction.

自己エネルギー汎関数法(self-energy functional approach)は、ラッティンジャー・ワードの定式化に基づく変分原理を利用して、対象とする系の自己エネルギーを変分的に決定する近似法である。ここで、試行関数の役割をする自己エネルギーは、"参照系"と呼ばれる容易に解くことのできる系で求める。すなわち、代理の系でパラメータを変化させて求めた自己エネルギーの中から、目的の系の物性を上手く再現するものを変分原理に基づいて探す。このとき、参照系は、対象とする系と同じ相互作用項を持つ必要がある。この方法の利点の一つに、参照系で求めた試行的な自己エネルギーを通して、相互作用の効果を非摂動論的に扱えることが挙げられる。また、ここで用いる変分原理は、系のグリーン関数が満たすべき因果律や保存則を保証する。これらの利点は、モット転移などの電子相関によって生じる様々な現象を調べるのに有効である。本稿では、自己エネルギー汎関数法について解説した後、モット転移に関する最近のトピックスについてこの方法を用いて行った研究を紹介する。

The superfluid-insulator transition of two-band fermionic atom systems in optical lattices is investigated by the two-site dynamical mean-field theory. Because of the spin-flip and pair-hopping interactions, orbital fluctuations are enhanced, leading to the suppression of the Mott insulating state. The numerical results are discussed in comparison with the effective boson model.

We study ultracold fermionic atoms loaded in an optical lattice with a confining potential. By combining dynamical mean-field approximation with a two-site impurity solver, we demonstrate that a supersolid state, where an s-wave superfluid coexists with a density-wave state of checkerboard pattern, is stabilized by attractive onsite interactions on a square lattice. The stability of the supersolid state in the thermodynamic limit is also addressed.

We study the multiband effects on ultracold fermionic atoms in optical lattices by two-site dynamical mean-field theory. We find that the density wave state becomes stable for a small orbital splitting region. As the orbital splitting is increased, the transition from the density wave state to the superfluid state occurs. By systematically changing the orbital splitting and the attractive interaction, we obtain the phase diagram at half-filling.

We investigate the single-particle dynamics and magnetic properties in the two-orbital Hubbard model on the square lattice at quarter filling by using a cluster extension of dynamical mean field theory. We find that the Fermi-liquid state is stabilized up to the large intra- and inter-orbital interactions in the symmetric case without Hund's coupling. It is clarified that the Hund's coupling enhances the antiferro-orbital fluctuations, which gives rise to the pseudo gap behavior in the single-particle excitations. We also find that the Hund's coupling with intermediate strength causes the competition between the Fermi-liquid formation and the antiferro-orbital fluctuations, resulting in the nonmonotonous temperature dependence in the single-particle dynamics.

We investigate the two-dimensional Hubbard model on the triangular lattice with anisotropic hopping integrals at half filling. By means of a self-energy functional approach, we discuss how stable the non-magnetic state is against magnetically ordered states in the system. We present the zero-temperature phase diagram, where the normal metallic state competes with magnetically ordered states with (pi, pi) and (2 pi/3, 2 pi/3) structures. It is shown that a nonmagnetic Mott insulating state is not realized as the ground state, in the present framework, but as a meta-stable state near the magnetically ordered phase with (2 pi/3, 2 pi/3) structure.

We study ultracold fermionic atoms trapped in an optical lattice with harmonic confinement by combining the real-space dynamical mean-field theory with a two-site impurity solver. By calculating the local particle density and the pair potential in the systems with different clusters, we discuss the stability of a supersolid state, where an s-wave superfluid coexists with a density-wave state of checkerboard pattern. It is clarified that a confining potential plays an essential role in stabilizing the supersolid state. The phase diagrams are obtained for several effective particle densities.

We Study the Kondo effect and related transport properties in orbitally degenerate vertical quantum dot systems with plural electrons. Applying the non-crossing approximation to the three-orbital Anderson impurity model with the finite Coulomb interaction and Hund-coupling, we investigate the magnetic-field dependence of the conductance and thermopower. We also introduce an additional orbital splitting to take account of the realistic many-body effect in the vertical quantum dot system. It is clarified how the three-orbital Kondo effect influences the transport properties via the modulation of the Kondo temperature and unitary limit of transport quantities due to the change of the symmetry in the system.

We study ultracold fermionic atoms trapped in an optical lattice with harmonic confinement by dynamical mean-field approximation. It is demonstrated that a supersolid state, where an s-wave superfluid coexists with a density-wave state with a checkerboard pattern, is stabilized by attractive onsite interactions on a square lattice. Our new finding here is that a confining potential plays an invaluable role in stabilizing the supersolid state. We establish a rich phase diagram at low temperatures, which clearly shows how an insulator, a density wave and a superfluid compete with each other to produce an interesting domain structure. Our results shed light on the possibility of the supersolid state in fermionic optical lattice systems.

Motivated by recent studies on the quasi-one-dimensional (1D) antiferromagnet BaCo2V2O8, we investigate the Tomonaga-Luttinger-liquid properties of the 1 D S = 1/2 XXZ Heisenberg-Ising model in magnetic fields. By using the Bethe ansatz solution, thermodynamic quantities and the divergence exponent of the NMR relaxation rate are calculated. We observe a magnetization minimum as a function of temperature (T) close to the critical field. As the magnetic field approaches the critical field, the minimum temperature asymptotically approaches the universal relation in agreement with the recent results by Maeda et al. We observe T-linear specific heat below the temperature of the magnetization minimum. The field dependence of its coefficient agrees with the results based on conformal field theory. The field dependence of the divergence exponent of the NMR relaxation rate with decreasing temperature is obtained, indicating a change in the critical properties. The results are discussed in connection with experiments on BaCo2V2O8.

The superfluid-insulator transition of fermionic atoms in optical lattices is investigated by two-site dynamical mean-field theory. It is shown that the Mott transition occurs as a result of multiband effects. The quasiparticle weight in the superfluid state decreases significantly as the system approaches the Mott transition point. By changing the interaction and the orbital splitting, we obtain the phase diagram at half filling. The numerical results are discussed in comparison with the effective boson model. © 2008 The American Physical Society.

The superfluid-insulator transition of fermionic atoms in optical lattices is investigated by two-site dynamical mean-field theory. It is shown that the Mott transition occurs as a result of multiband effects. The quasiparticle weight in the superfluid state decreases significantly as the system approaches the Mott transition point. By changing the interaction and the orbital splitting, we obtain the phase diagram at half filling. The numerical results are discussed in comparison with the effective boson model.

We study the three-orbital Kondo effect in quantum dot (QD) systems by applying the non-crossing approximation to the three-orbital Anderson impurity model. By investigating the tunneling conductance through a QD, we show that the competition between the Hund-coupling and the orbital level-splitting gives rise to characteristic behavior in transport properties. It is found that the Hund-coupling becomes more important in the three-orbital case than in the two-orbital case. We also show that; the enhancement of Kondo temperature due to the singlet-triplet mechanism suggested for the two-orbital model tends to be suppressed by the existence of the third orbital.

We investigate the Kondo effect of a multiorbital quantum dot coupled to spin polarized leads, using the noncrossing approximation. It is shown that as the spin polarization is increased, the Kondo peak splits into three peaks and the middle one is located close to the Fermi energy. The results indicate that the Kondo effect caused by the orbital degrees of freedom survives, while the Kondo effect by the spin degrees of freedom is suppressed. In the temperature dependence of the conductance, the hump structure emerges owing to the contribution from the orbital and spin degrees of freedom. (c) 2007 Elsevier B.V. All rights reserved.

We review the results of specific-heat experiments on the S = 1 quasi-one-dimensional (quasi-1D) bond-alternating antiferromagnet Ni(C9H24N4)(NO2)ClO4, alias NTENP. At low temperatures above the transition temperature of a field-induced long-range order, the magnetic specific heat (C-mag) of this compound becomes proportional to temperature (T), when a magnetic field along the spin chains exceeds the critical field H-c at which the energy gap vanishes. The ratio C-mag / T, which increases as the magnetic field approaches H-c from above, is in good quantitative agreement with a prediction of conformal field theory combined with the field-dependent velocity of the excitations calculated by the Lanczos method. This result is the first conclusive evidence for a Tomonaga-Luttinger liquid in a gapped quasi-1D antiferromagnet.

We study the magnetic properties around the Mott transition in the Kagome lattice Hubbard model by using the cellular dynamical mean field theory combined with quantum Monte Carlo simulations. By investigating the q-dependence of the susceptibility, we find a dramatic change in the dominant spin fluctuations around the Mott transition. The spin fluctuations in the insulating phase favour down to the lowest temperature a spatial spin configuration in which antiferromagnetic correlations are strong only in one chain direction but almost vanishing in the others.