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We study finite-temperature properties of a Hubbard model including sites of a particle bath which was proposed as a microscopic model to show itinerant ferromagnetism at finite electron density. We use direct numerical methods, such as exact diagonalization and random vector methods. The temperature dependence of quantities is surveyed in the full range of the temperature. We find that the specific heat has several peaks, which correspond to ordering processes in different energy scales. In particular, magnetic order appears at very low temperature. Depending on the chemical potential of the particle bath and the Coulomb interaction, the system exhibits an itinerant ferromagnetic state or an antiferromagnetic state of the Mott insulator. Microscopically the competition between these two types of orderings causes a peculiar ordering process of local spin correlations. Some local ferromagnetic correlations are found to be robust, which indicates that the ferromagnetic correlation originates from the motion of itinerant electrons in a short-range cluster., Comment: 13 pages, 13 figures

We investigate magnetic excitations and spin transport properties of a frustrated spin chain with ferromagnetic nearest-neighbor and antiferromagnetic next-nearest-neighbor exchange couplings in a magnetic field by density-matrix renormalization group methods. In the field-induced quadrupole and octupole regimes, the low-energy excitation is governed by two- and three-magnon bound states, respectively, so that bound magnon clusters would contribute to the spin transport. We show that spin current correlations decrease when the system goes from the quadrupole regime into the octupole regime. This indicates that the spin transport is suppressed in the octupole regime, although bound three-magnon clusters carry a larger amount of angular momentum than bound two-magnon clusters., Comment: 6 pages, 4 figures, Proceedings of CCP2021 (August 1-5, 2021, Coventry, UK, online)

To clarify the transport property mediated by bound magnons in a spin nematic state, we investigate the spin Drude weight of a spin-1/2 $J_{1}$-$J_{2}$ Heisenberg chain with ferromagnetic $J_{1}$ and antiferromagnetic $J_{2}$ in a magnetic field by numerical diagonalization. At zero magnetic field, numerical results with up to 24 sites suggest that the spin Drude weight would be zero in the thermodynamic limit, indicating diffusive spin transport. With increasing the magnetic field, the spin Drude weight is enhanced at low temperatures, indicating that bound magnons would contribute to the spin transport., Comment: 7 pages, 4 figures, Proceedings of JEMS2018 (September 3-7, 2018, Mainz, Germany)

We investigate the dynamical quadrupole structure factor of a spin-1/2 $J_{1}$-$J_{2}$ Heisenberg chain with competing ferromagnetic $J_{1}$ and antiferromagnetic $J_{2}$ in a magnetic field by exploiting density-matrix renormalization group techniques. In a field-induced spin nematic regime, we observe gapless excitations at $q=\pi$ according to quasi-long-range antiferro-quadrupole correlations. The gapless excitation mode has a quadratic form at the saturation, while it changes into a linear dispersion as the magnetization decreases., Comment: 7 pages, 3 figures, Proceedings of SCES2017 (September 17-21, 2017, Prague, Czech Republic)

The nuclear and magnetic structure and full magnon dispersions of yttrium iron garnet Y$_3$Fe$_5$O$_{12}$ have been studied by neutron scattering. The refined nuclear structure is distorted to a trigonal space group of $R\bar{3}$. The highest-energy dispersion extends up to 86 meV. The observed dispersions are reproduced by a simple model with three nearest-neighbor-exchange integrals between 16$a$ (octahedral) and 24$d$ (tetrahedral) sites, $J_{aa}$, $J_{ad}$, and $J_{dd}$, which are estimated to be 0.00$\pm$0.05, $-$2.90$\pm$0.07, and $-$0.35$\pm$0.08 meV, respectively. The lowest-energy dispersion below 14 meV exhibits a quadratic dispersion as expected from ferromagnetic magnons. The imaginary part of $q$-integrated dynamical spin susceptibility $\chi$"($E$) exhibits a square-root energy-dependence in the low energies. The magnon density of state is estimated from the $\chi$"($E$) obtained on an absolute scale. The value is consistent with a single polarization mode for the magnon branch expected theoretically., Comment: 9 pages, 9 figures

The spin-1 Haldane chain is an example of the symmetry-protected-topological (SPT) phase in one dimension. Experimental realization of the spin chain materials usually involves both the uniaxial-type, $D(S^z)^2$, and the rhombic-type, $E[(S^x)^2-(S^y)^2]$, single-ion anisotropies. Here, we provide a precise ground-state phase diagram for spin-1 Haldane chain with these single-ion anisotropies. Using quantum numbers, we find that the $\mathbb{Z}_2$ symmetry breaking phase can be characterized by double degeneracy in the entanglement spectrum. Topological quantum phase transitions take place on particular paths in the phase diagram, from the Haldane phase to the Large-$E_x$, Large-$E_y$, or Large-$D$ phases. The topological critical points are determined by the level spectroscopy method with a newly developed parity technique in the density matrix renormalization group [Phys. Rev. B 86, 024403 (2012)], and the Haldane-Large-$D$ critical point is obtained with an unprecedentedly precision, $(D/J)_c=0.9684713(1)$. Close to this critical point, a small rhombic single-ion anisotropy $|E|/J\ll1$ can destroy the Haldane phase and bring the system into a $y$-N\'eel phase. We propose that the compound [Ni(HF$_2$)(3-Clpy)$_4$]BF$_4$ is a candidate system to search for the $y$-N\'eel phase., Comment: Supplemental Material is included

We propose a variational wavefunction containing parameters to tune the probabilities of all the possible onsite configurations for the periodic Anderson model. We call it the full onsite-correlation wavefunction (FOWF). This is a simple extension of the Gutzwiller wavefunction (GWF), in which one parameter is included to tune the double occupancy of the f electrons at the same site. We compare the energy of the GWF and the FOWF evaluated by the variational Monte Carlo method and that obtained with the density-matrix renormalization group method. We find that the energy is considerably improved in the FOWF. On the other hand, the physical quantities do not change significantly between these two wavefunctions as long as they describe the same phase, such as the paramagnetic phase. From these results, we not only demonstrate the improvement by the FOWF, but we also gain insights on the applicability and limitation of the GWF to the periodic Anderson model., Comment: 5 pages, 5 figures, to be published in J. Phys. Soc. Jpn

By exploiting density-matrix renormalization group techniques, we investigate the spin dynamics of a spin-1/2 one-dimensional J1-J2 XXZ model with competing ferromagnetic J1 and antiferromagnetic J2 exchange couplings under applied magnetic fields. Numerical results of spin excitation spectra show that in the field-induced spin quadrupole regime, the longitudinal component has a gapless mode and the transverse component has a gapped mode irrespective of the exchange anisotropy. The excitation gap of the transverse spin excitation increases as the exchange anisotropy increases over the XY-like and Ising-like regions, demonstrating that two-magnon bound states are stabilized due to the easy-axis anisotropy., Comment: 6 pages, 3 figures, Proceedings of SCES2014 (July 7-11, 2014, Grenoble, France)

By exploiting density-matrix renormalization group techniques, we investigate the dynamical spin structure factor of a spin-1/2 Heisenberg chain with ferromagnetic nearest-neighbor and antiferromagnetic next-nearest-neighbor exchange interactions in an applied magnetic field. In a field-induced spin nematic regime, we find gapless longitudinal and gapped transverse spin excitation spectra, in accordance with quasi-long-ranged longitudinal and short-ranged transverse spin correlations, respectively. The gapless point coincides with the dominant longitudinal spin correlation, whereas the gap position exhibits a characteristic field dependence contradicting the dominant transverse spin correlation., Comment: 4 pages, 5 figures, To appear in J. Phys. Soc. Jpn

Inspired by the Nagaoka ferromagnetism, we propose an itinerant model to study the transition between the Mott singlet state and a ferromagnetic state by emulating a doping process in finite lattices. In the Nagaoka ferromagnetism, the total spin of the system takes the maximum value when an electron is removed from the half-filled system. To incorporate a procedure of the electron removal, our model contains extra sites as a reservoir of electrons, and the chemical potential of the reservoir controls the distribution of electrons. As a function of the chemical potential, the system exhibits ground-state phase transitions among various values of the total spin, including a saturated ferromagnetic state due to the Nagaoka mechanism at finite hole density. We discuss the nature of the ferromagnetism by measuring various physical quantities, such as the distribution of electrons, the spin correlation functions, the magnetization process in the magnetic field, and also the entanglement entropy., Comment: 12 pages, 16 figures

To clarify a crucial role of a spin-orbit coupling in the emergence of novel spin-orbital states in $5d$-electron compounds such as Sr$_{2}$IrO$_{4}$, we investigate ground state properties of a $t_{\rm 2g}$-orbital Hubbard model on a square lattice by Lanczos diagonalization. In the absence of the spin-orbit coupling, the ground state is spin singlet. When the spin-orbit coupling is strong enough, the ground state turns into a weak ferromagnetic state. The weak ferromagnetic state is a singlet state in terms of an effective total angular momentum. Regarding the orbital state, we find the so-called complex orbital state, in which real $xy$, $yz$, and $zx$ orbital states are mixed with complex coefficients., Comment: 4 pages, 3 figures, Proceedings of SCES2011 (August 29 - September 3, 2011, Cambridge, UK)

To clarify a key role of orbital degrees of freedom in the response of the many-body electron state of correlated electrons to an external field, we investigate the real-time dynamics in an $e_{\rm g}$-orbital Hubbard model under applied electric fields by exploiting numerical techniques such as a time-dependent density-matrix renormalization group (DMRG) method. The ground state without applying an electric field is found to be an antiferromagnetic/ferro-orbital state. After we switch on an oscillating electric field, it gives rise to the creation of holon-doublon pairs when the frequency of the applied electric field exceeds a charge excitation gap. We argue that a pair-hopping process yields a dynamical deformation of the orbital configuration., Comment: 4 pages, 4 figures, Proceedings of QCNP2012 (August 26-29, 2012, Dresden, Germany)

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., Comment: 5 pages, 3 figures, Proceedings of SCES2013 (August 5-9, 2013, Tokyo, Japan)

We study the real-time evolution of a charge-excited state in a one-dimensional $e_{\rm g}$-orbital degenerate Hubbard model, by a time-dependent density-matrix renormalization group method. Considering a chain along the $z$ direction, electrons hop between adjacent $3z^2-r^2$ orbitals, while $x^2-y^2$ orbitals are localized. For the charge-excited state, a holon-doublon pair is introduced into the ground state at quarter filling. At initial time, there is no electron in a holon site, while a pair of electrons occupies $3z^2-r^2$ orbital in a doublon site. As the time evolves, the holon motion is governed by the nearest-neighbor hopping, but the electron pair can transfer between $3z^2-r^2$ orbital and $x^2-y^2$ orbital through the pair hopping in addition to the nearest-neighbor hopping. Thus holon and doublon propagate at different speed due to the pair hopping that is characteristic of multi-orbital systems., Comment: 4 pages, 3 figures, Proceedings of ICM2009 (July 26-31, 2009, Karlsruhe, Germany)

We investigate the ground-state properties of a one-dimensional $t_{\rm 2g}$-orbital Hubbard model including an atomic spin-orbit coupling by using numerical methods, such as Lanczos diagonalization and density-matrix renormalization group. As the spin-orbit coupling increases, we find a ground-state transition from a paramegnetic state to a ferromagnetic state. In the ferromagnetic state, since the spin-orbit coupling mixes spin and orbital states with complex number coefficients, an antiferro-orbital state with complex orbitals appears. According to the appearance of the complex orbital state, we observe an enhancement of $\Gamma_{4u}$ octupole correlations., Comment: 3 pages, 3 figures, To appear in J. Phys. Soc. Jpn. Suppl., Proceedings of ICHE2010 (September 17-20, 2010, Hachioji, Japan)

To clarify a key role of $f$ orbitals in the emergence of antiferro-quadrupole structure in PrPb$_{3}$, we investigate the ground-state property of an orbital-degenerate Kondo lattice model by numerical diagonalization techniques. In PrPb$_{3}$, Pr$^{3+}$ has a $4f^{2}$ configuration and the crystalline-electric-field ground state is a non-Kramers doublet $\Gamma_{3}$. In a $j$-$j$ coupling scheme, the $\Gamma_{3}$ state is described by two local singlets, each of which consists of two $f$ electrons with one in $\Gamma_{7}$ and another in $\Gamma_{8}$ orbitals. Since in a cubic structure, $\Gamma_{7}$ has localized nature, while $\Gamma_{8}$ orbitals are rather itinerant, we propose the orbital-degenerate Kondo lattice model for an effective Hamiltonian of PrPb$_{3}$. We show that an antiferro-orbital state is favored by the so-called double-exchange mechanism which is characteristic of multi-orbital systems., Comment: 3 pages, 3 figures, Proceedings of Skutterudite2007 (September 26-30, 2007, Kobe)

We investigate the ground-state property and the excitation gap of a one-dimensional spin-orbital model with isotropic spin and anisotropic orbital exchange interactions, which represents the strong-coupling limit of a two-orbital Hubbard model including the Hund's rule coupling ($J$) at quarter filling, by using a density-matrix renormalization group method. At J=0, spin and orbital correlations coincide with each other with a peak at $q=\pi/2$, corresponding to the SU(4) singlet state. On the other hand, spin and orbital states change in a different way due to the Hund's rule coupling. With increasing $J$, the peak position of orbital correlation changes to $q=\pi$, while that of spin correlation remains at $q=\pi/2$. In addition, orbital dimer correlation becomes robust in comparison with spin dimer correlation, suggesting that quantum orbital fluctuation is enhanced by the Hund's rule coupling. Accordingly, a relatively large orbital gap opens in comparison with a spin gap, and the system is described by an effective spin system on the background of the orbital dimer state., Comment: 8 pages, 9 figures

We investigate the ground-state property of a one-dimensional two-orbital Hubbard model at quarter filling by numerical techniques such as the density-matrix renormalization group method and the exact diagonalization. When the Hund's rule coupling $J$ is zero, the model is SU(4) symmetric. In fact, both spin and orbital correlations have a peak at $q=\pi/2$, indicating an SU(4) singlet state with a four-site periodicity. On the other hand, with increasing $J$, it is found that the peak position of the orbital correlation changes to $q=\pi$, while that of the spin correlation remains at $q=\pi/2$. We briefly discuss how the SU(4) symmetry is broken by $J$., Comment: 2 pages, 2 figures, Proceedings of ICM2006 (August 20-25, 2006, Kyoto)

In order to discuss the spin-gap formation in a multiorbital system, we analyze an e_g-orbital Hubbard model on a geometrically frustrated zigzag chain by using a density-matrix renormalization group method. Due to the appearance of a ferro-orbital arrangement, the system is regarded as a one-orbital system, while the degree of spin frustration is controlled by the spatial anisotropy of the orbital. In the region of strong spin frustration, we observe a finite energy gap between ground and first-excited states, which should be called a spin-orbital gap. The physical meaning is clarified by an effective Heisenberg spin model including correctly the effect of the orbital arrangement influenced by the spin excitation., Comment: 8 pages, 6 figures, extended version

By using a density matrix renormalization group method, we investigate the ground-state properties of a one-dimensional three-orbital Hubbard model on the basis of a j-j coupling scheme. For $B_4^0 \ne 0$, where $B_4^0$ is a parameter to control cubic crystalline electric field effect, one orbital is itinerant, while other two are localized. Due to the competition between itinerant and localized natures, we obtain orbital ordering pattern which is sensitive to $B_4^0$, leading to a characteristic change of $\Gamma_{3g}$ quadrupole state into an incommensurate structure. At $B_4^0 = 0$, all the three orbitals are degenerate, but we observe a peak at $q = 0$ in $\Gamma_{3g}$ quadrupole correlation, indicating a ferro-orbital state, and the peak at $q = \pi$ in $\Gamma_{4u}$ dipole correlation, suggesting an antiferromagnetic state. We also discuss the effect of $\Gamma_{4u}$ octupole on magnetic anisotropy., Comment: 4 pages, 3 figures, Proceedings of ASR-WYP-2005 (September 27-29, 2005, Tokai)

We investigate the ground-state properties of a t2g-orbital Hubbard model on a triangular lattice at electron density 5.5 by using numerical techniques. There appear several types of paramagnetic phases, but we observe in common that one or two orbitals among three orbitals become relevant due to the effect of orbital arrangement. It is found that charge stripes stabilized by the nearest-neighbor Coulomb interaction consist of antiferromagnetic/ferro-orbital chains for small Hund's coupling, while there occurs stripe charge ordering with ferromagnetic/antiferro-orbital chains for large Hund's coupling., Comment: 2 pages, 2 figures, Proceedings of LT24 (August 10-17, 2005, Orlando)

We present the zero-temperature phase diagram of the one-dimensional t2g-orbital Hubbard model, obtained using the density-matrix renormalization group and Lanczos techniques. Emphasis is given to the case for the electron density n=5 corresponding to five electrons per site, of relevance for some Co-based compounds. However, several other cases for electron densities between n=3 and 6 are also studied. At n=5, our results indicate a first-order transition between a paramagnetic (PM) insulator phase and a fully-polarized ferromagnetic (FM) state by tuning the Hund's coupling. The results also suggest a transition from the n=5 PM insulator phase to a metallic regime by changing the electron density, either via hole or electron doping. The behavior of the spin, charge, and orbital correlation functions in the FM and PM states are also described in the text and discussed. The robustness of these two states varying parameters suggests that they may be of relevance in more realistic higher dimensional systems as well., Comment: 9 pages, 8 figures

We investigate the ground-state property of an e_g-orbital Hubbard model at quarter filling on a zigzag chain by exploiting the density matrix renormalization group method. When two orbitals are degenerate, the zigzag chain is decoupled to a doble-chain spin system to suppress the spin frustration due to the spatial anisotropy of the occupied orbital. On the other hand, when the level splitting is increased and the orbital anisotropy disappears, a characteristic change in the spin incommnsurability is observed due to the revival of the spin frustration., Comment: 2 pages, 1 figure, Proceedings of SCES'05 (July 26-30, 2005, Vienna)

In order to understand a crucial role of orbital degree of freedom in the magnetic structure of recently synthesized neptunium compounds NpTGa_5 (T=Fe, Co, and Ni), we propose to discuss the magnetic phase of an effective two-orbital model, which has been constructed based on a j-j coupling scheme to explain the magnetic structure of uranium compounds UTGa_5. By analyzing the model with the use of numerical technique such as exact diagonalization, we obtain the phase diagram including several kinds of magnetic states. An orbital-based scenario is discussed to understand the change in the magnetic structure among C-, A-, and G-type antiferromagnetic phases, experimentally observed in NpFeGa_5, NpCoGa_5, and NpNiGa_5., Comment: 18 pages, 8 figures, to appear in New Journal of Physics

In order to clarify a crucial role of orbital degree of freedom in geometrically frustrated systems, we investigate both ground- and excited-state properties of the e_g-orbital degenerate Hubbard model on two kinds of lattices, ladder and zigzag chain, by using numerical techniques. In the ladder, spin correlation extends on the whole system, while the zigzag chain is decoupled to a double chain and spin excitation is confined in one side of the double chain due to the selection of a specific orbital. We envision a kind of self-organization phenomenon that the geometrically frustrated multi-orbital system is spontaneously reduced to a one-orbital model to suppress the spin frustration., Comment: 4 pages, 4 figures

In order to clarify a key role of orbital degree of freedom in the spin S=1 Haldane system, we investigate ground-state properties of the t2g-orbital degenerate Hubbard model on the linear chain by using numerical techniques. Increasing the Hund's rule coupling in multi-orbital 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 orbital degree of freedom. Possible relevance of the present results to actual systems is also discussed., Comment: 4 pages, 3 figures, to appear in Phys. Rev. B

By using the density matrix renormalization group method, we investigate ground- and excited-state properties of the e_g-orbital degenerate Hubbard model at quarter filling for two kinds of lattices, zigzag chain and ladder. In the zigzag chain, the system is effectively regarded as a decoupled double chain of the S=1/2 antiferromagnetic Heisenberg model, and the spin gap is approximately zero, similar to the case of weakly coupled Heisenberg chains. On the other hand, in the ladder, the spin correlation on the rung remains robust and the spin gap exists., Comment: 2 pages, 2 figures, Proceedings of SCES'04 (July 26-30, 2004, Karlsruhe)

We investigate a one-dimensional S=1/2 antiferromagnetic Heisenberg model coupled to quantum lattice vibration using a quantum Monte Carlo method. We study the ground-state lattice fluctuation where the system shows a characteristic structure factor. We also study the mass dependence of magnetic properties such as the magnetic susceptibility and the magnetic excitation spectrum. For heavy mass, the system shows the same behavior as the case of classical lattice vibration. On the other hand, for light mass, magnetic properties coincide with those of the static uniform chain. We investigate the physical mechanism of this behavior and propose the picture of quantum narrowing., Comment: 7 pages, 16 eps figures embedded in the text; added comments in section 3, corrected typos

We investigate a one-dimensional S=1 antiferromagnetic Heisenberg model coupled to a lattice distortion by a quantum Monte Carlo method. Investigating the ground state energy of the static bond-alternating chain, we find that the instability to a dimerized chain depends on the value of the spin-phonon coupling, unlike the case of S=1/2. The spin state is the dimer state or the uniform Haldane state depending on whether the lattice distorts or not, respectively. At an intermediate value of the spin-phonon coupling, we find the first-order transition between the two states. We also find the coexistence of the two states., Comment: 7 pages, 12 eps figures embedded in the text; corrected typos, replaced figures

We investigate thermodynamic properties of a one-dimensional S=1/2 antiferromagnetic Heisenberg model coupled to a lattice distortion by a quantum Monte Carlo method. In particular we study how spin and lattice dimerize as a function of the temperature, which gives a fundamental process of the spin-Peierls transition in higher dimensions. The degree of freedom of the lattice is taken into account adiabatically and the thermal distribution of the lattice distortion is obtained by the thermal bath algorithm. We find that the dimerization develops as the temperature decreases and it converges to the value of the dimerization of the ground state at T=0. Furthermore we find that the coupling constants of spins fluctuate quite largly at high temperature and there thermodynamic properties deviate from those of the uniform chain. Doping of non-magnetic impurities causes cut of the chain into short chains with open boundary. We investigate thermodynamic properties of open chains taking relaxation of the lattice into consideration. We find that strong bonds locate at the edges and a defect of the bond alternation appears in the chain with odd number of sites, which causes enhancement of the staggered magnetic order. We find a spreaded staggered structure which indicates that the defect moves diffusively in the chain even at very low temperature., Comment: 7 pages, 17 figures; added comments on section 2 and 3, corrected typos

We study the magnetic properties of $S=1/2$ antiferromagnetic Heisenberg chains with inhomogeneity of interaction. Using a quantum Monte Carlo method and an exact diagonalization method, we study bond-impurity effect in the uniform $S=1/2$ chain and also in the bond-alternating chain. Here `bond impurity' means a bond with strength different from those in the bulk or a defect in the alternating order. Local magnetic structures induced by bond impurities are investigated both in the ground state and at finite temperatures, calculating the local magnetization, the local susceptibility and the local field susceptibility. We also investigate the force acting between bond impurities and find the force generally attractive., Comment: 15pages, 34figures

A quantum Monte Carlo method combining update of the loop algorithm with the global flip of the world line is proposed as an efficient method to study the magnetization process in an external field, which has been difficult because of inefficiency of the update of the total magnetization. The method is demonstrated in the one dimensional antiferromagnetic Heisenberg model and the trimer model. We attempted various other Monte Carlo algorithms to study systems in the external field and compared their efficiency., Comment: 5 pages, 9 figures; added references for section 1, corrected typos