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T. Fujiwara

Publications and source records attributed to T. Fujiwara.

At least 37 records · Page 2Linked to original sources
arXiv2009

On a weighted quasi-residual minimization strategy of the QMR method for solving complex symmetric shifted linear systems

We consider the solution of complex symmetric shifted linear systems. Such systems arise in large-scale electronic structure simulations and there is a strong need for the fast solution of the systems. With the aim of solving the systems efficiently, we consider a special case of the QMR method for non-Hermitian shifted linear systems and propose its weighted quasi-minimal residual approach. A numerical algorithm, referred to as shifted QMR\_SYM($B$), is given by the choice of a particularly cost-effective weight. Numerical examples are presented to show the performance of the shifted QMR\_SYM($B$) method.

math.NA↗
arXiv2008

Topological meaning of Z$_2$ numbers in time reversal invariant systems

We show that the Z$_2$ invariant, which classifies the topological properties of time reversal invariant insulators, has deep relationship with the global anomaly. Although the second Chern number is the basic topological invariant characterizing time reversal systems, we show that the relative phase between the Kramers doublet reduces the topological quantum number Z to Z$_2$.

cond-mat.mes-hall↗
arXiv2008

GW approximation with LSDA+U method and applications to NiO, MnO, and V$_2$O$_3$

A GW approximation (GWA) method named U+GWA is proposed, where we can start GWA with more localized wave functions obtained by the local spin-density approximation (LSDA)+U method. Then GWA and U+GWA are applied to MnO, NiO, and V$_2$O$_3$ in antiferromagnetic phase. The band gaps and energy spectra show an excellent agreement with the experimentally observed results and are discussed in details. The calculated width of d-bands of V$_2$O$_3$ is much narrower than that of the observed one which may be a mixture of t$_{2g}^2$ multiplet and single electron t$_{2g}$ level. GWA or U+GWA does not work also in the paramagnetic phase of V$_2$O$_3$ and the reason for thois is clarified. The method of the unique choice of on-site Coulomb interaction is discussed in details. The criterion for whether we should adopt GWA or U+GWA is discussed and is assessed with the help of the off-diagonal elements of the self-energy.

cond-mat.str-el↗
arXiv2007

Charge and spin stripe in La$_{2-x}$Sr$_{x}$NiO$_{4}$ (x=1/3,1/2)

Electronic structure of stripe ordered La$_{2-x}$Sr$_{x}$NiO$_{4}$ is investigated. The system with x=1/3 is insulator, in LSDA+U calculations, and shows charge and spin stripe, consistent with the experimental results. Highly correlated system of x=1/2 is studied by using exact diagonalization of multi-orbital many body Hamiltonian derived from LDA calculations and including on-site and inter-site Coulomb interactions. The fluctuation of the residual spin on Ni$^{3+}$ (hole) site couples with the charge fluctuation between Ni$^{3+}$ and Ni$^{2+}$ states and this correlation lowers the total energy. The resultant ground state is insulator with charge and spin stripe of the energy gap 0.9eV, consistent with observed one. The on-site Coulomb interaction stabilizes integral valency of each Ni ion (Ni$^{3+}$ and Ni$^{2+}$), but does not induce the charge order. Two quantities, inter-site Coulomb interaction and anisotropy of hopping integrals, play an important role to form the charge and spin stripe order in a system of x=1/2.

cond-mat.str-el↗
arXiv2007

NMR Study on the Vortex Slush Phase in Organic Superconductor κ-(BEDT-TTF)2Cu(NCS)2

The vortex state in a single crystal of the layered organic superconductor κ-(BEDT-TTF2Cu(NCS)2, where BEDT-TTF (or ET) is bis(ethylenedithio)tetrathiafulvalene, was studied by 1H-NMR. Under a low field region around 0.75 T, the vortex glass-liquid transition was demonstrated by a diverging of the longitudinal nuclear spin relaxation rate and peak-broadening in spectra. Under a high field region near the upper critical field Hc2(0)~7 T, the curvature of nuclear spin relaxation curves showed a drastic change at the temperature where the emergence of the quantum vortex slush state was reported. The mechanism in this curvature change was discussed in terms of the fluctuating field produced by fragments of vortex glass.

cond-mat.str-el↗
arXiv2006

Cu-NMR study on the disordered quantum spin magnet with the Bose-glass ground state

Cu-NMR study has been performed on the disordered spin-gap system Tl1-xKxCuCl3 In the high-field H > HC=Δ/μ_B, where Δis the spin-gap, the hyperfine field becomes extremely inhomogeneous at low temperatures due to the field-induced magnetic order, indicating that the ordered spin state must be different from the pure TlCuCl3. In the low field H < HC, a saturating behavior in the longitudinal nuclear spin relaxation rate 1/T1 was observed at low temperatures, indicating existence of the magnetic ground state proposed to be Bose-glass phase by Fisher.

cond-mat.str-el↗
arXiv2006

Linear Algebraic Calculation of Green's function for Large-Scale Electronic Structure Theory

A linear algebraic method named the shifted conjugate-orthogonal-conjugate-gradient method is introduced for large-scale electronic structure calculation. The method gives an iterative solver algorithm of the Green's function and the density matrix without calculating eigenstates.The problem is reduced to independent linear equations at many energy points and the calculation is actually carried out only for a single energy point. The method is robust against the round-off error and the calculation can reach the machine accuracy. With the observation of residual vectors, the accuracy can be controlled, microscopically, independently for each element of the Green's function, and dynamically, at each step in dynamical simulations. The method is applied to both semiconductor and metal.

cond-mat.mtrl-sci↗
arXiv2005

Electronic structure of A-type antiferomagnetic LaMnO_3 by GW approximation

The electronic structure of the A-type antiferromagnetic insulator LaMnO3 is investigated by the GW approximation. The band gap and spectrum are in a good agreement with experimental observation. The on-site/off-site dynamical screened Coulomb interaction on Mn sites is also calculated. Comparison with the results by the Hartree-Fock and the static COHSEX approximations is discussed in detail. The dynamical screening effect is important for the band gap and widths.

cond-mat.str-el↗
arXiv2005

Large-scale electronic-structure theory and nanoscale defects formed in cleavage process of silicon

Several methods are constructed for large-scale electronic structure calculations. Test calculations are carried out with up to 10^7 atoms. As an application, cleavage process of silicon is investigated by molecular dynamics simulation with 10-nm-scale systems. As well as the elementary formation process of the (111)-(2 x 1) surface, we obtain nanoscale defects, that is, step formation and bending of cleavage path into favorite (experimentally observed) planes. These results are consistent to experiments. Moreover, the simulation result predicts an explicit step structure on the cleaved surface, which shows a bias-dependent STM image.

cond-mat.mtrl-sci↗
arXiv2003

Higher orders of the high-temperature expansion for the Ising model in three dimensions

The new algorithm of the finite lattice method is applied to generate the high-temperature expansion series of the simple cubic Ising model to $β^{50}$ for the free energy, to $β^{32}$ for the magnetic susceptibility and to $β^{29}$ for the second moment correlation length. The series are analyzed to give the precise value of the critical point and the critical exponents of the model.

hep-lat↗
arXiv2002

New algorithm of the high-temperature expansion for the Ising model in three dimensions

New algorithm of the finite lattice method is presented to generate the high-temperature expansion series of the Ising model. It enables us to obtain much longer series in three dimensions when compared not only to the previous algorithm of the finite lattice method but also to the standard graphical method. It is applied to extend the high-temperature series of the simple cubic Ising model from beta^{26} to beta^{46} for the free energy and from beta^{25} to beta^{32} for the magnetic susceptibility.

hep-lat↗
arXiv2002

Spectrum of the Hermitian Wilson-Dirac Operator for a Uniform Magnetic Field in Two Dimensions

It is shown that the eigenvalue problem for the hermitian Wilson-Dirac operator of for a uniform magnetic field in two dimensions can be reduced to one-dimensional problem described by a relativistic analog of the Harper equation. An explicit formula for the secular equations is given in term of a set of polynomials. The spectrum exhibits a fractal structure in the infinite volume limit. An exact result concerning the index theorem for the overlap Dirac operator is obtained.

hep-lat↗
arXiv2001

A Numerical Study of Spectral Flows of Hermitian Wilson-Dirac Operator and the Index Theorem in Abelian Gauge Theories on Finite Lattices

We investigate the index of the Neuberger's Dirac operator in abelian gauge theories on finite lattices by numerically analyzing the spectrum of the hermitian Wilson-Dirac operator for a continuous family of gauge fields connecting different topological sectors. By clarifying the characteristic structure of the spectrum leading to the index theorem we show that the index coincides to the topological charge for a wide class of gauge field configurations. We also argue that the index can be found exactly for some special but nontrivial configurations in two dimensions by directly analyzing the spectrum.

hep-lat↗
arXiv2000

Topological Obstruction in Block-spin Transformations

Block-spin transformations from a fine lattice to a coarse one are shown to give rise to a one-to-one correspondence between the zero-modes of the Ginsparg-Wilson Dirac operators. The index is then preserved under the blocking process. Such a one-to-one correspondence is violated and the block-spin transformation becomes necessarily ill-defined when the absolute value of the index is larger than 2rN, where N is the number of the sites on the coarse lattice and r is the dimension of the gauge group representation of the fermion variables.

hep-lat↗
arXiv2000

Topological Charge of Lattice Abelian Gauge Theory

Configuration space of abelian gauge theory on a periodic lattice becomes topologically disconnected by excising exceptional gauge field configurations. It is possible to define a U(1) bundle from the nonexceptional link variables by a smooth interpolation of the transition functions. The lattice analogue of Chern character obtained by a cohomological technique based on the noncommutative differential calculus is shown to give a topological charge related to the topological winding number of the U(1) bundle.

hep-lat↗
arXiv1999

The origin and formation of cuspy density profiles through violent relaxation of stellar systems

It is shown that the cuspy density distributions observed in the cores of elliptical galaxies can be realized by dissipationless gravitational collapse. The initial models consist of power-law density spheres such as $ρ\propto r^{-1}$ with anisotropic velocity dispersions. Collapse simulations are carried out by integrating the collisionless Boltzmann equation directly, on the assumption of spherical symmetry. From the results obtained, the extent of constant density cores, formed through violent relaxation, decreases as the velocity anisotropy increases radially, and practically disappears for extremely radially anisotropic models. As a result, the relaxed density distributions become more cuspy with increasing radial velocity anisotropy. It is thus concluded that the velocity anisotropy could be a key ingredient for the formation of density cusps in a dissipationless collapse picture. The velocity dispersions increase with radius in the cores according to the nearly power-law density distributions. The power-law index, $n$, of the density profiles, defined as $ρ\propto r^{-n}$, changes from $n\approx 2.1$ at intermediate radii, to a shallower power than $n\approx 2.1$ toward the centre. This density bend can be explained from our postulated local phase-space constraint that the phase-space density accessible to the relaxed state is determined at each radius by the maximum phase-space density of the initial state.

astro-ph↗