arXiv subjects

Noboru Fukushima

Publications and source records attributed to Noboru Fukushima.

13 recordsLinked to original sources

arXiv2011

Renormalization of transition matrix elements of particle number operators due to strong electron correlation

Renormalization of non-magnetic and magnetic impurities due to electron double occupancy prohibition is derived analytically by an improved Gutzwiller approximation. Non-magnetic impurities are effectively weakened by the same renormalization factor as that for the hopping amplitude, whereas magnetic impurities are strengthened by the square root of the spin-exchange renormalization factor, in contrast to results by the conventional Gutzwiller approximation. We demonstrate it by showing that transition matrix elements of number operators between assumed excited states and between an assumed ground state and excited states are renormalized differently than diagonal matrix elements. Deviation from such simple renormalization with a factor is also discussed. In addition, as related calculation, we correct an error in treatment of renormalization of charge interaction in the literature. Namely, terms from the second order of the transition matrix elements are strongly suppressed. Since all these results do not depend on the signs of impurity potential or charge interaction parameter, they are valid both in attractive and repulsive cases.

cond-mat.str-el↗

arXiv2009

Impurity Potential Renormalization by Strong Electron Correlation

Renormalization of non-magnetic impurity potential by strong electron correlation is investigated in detail. We adopt the t-t'-t"-J model and consider mainly a delta-function impurity potential. The variational Monte Carlo method shows that impurity potential scattering matrix elements between Gutzwiller-projected quasi-particle excited states are as strongly renormalized as the hopping terms. Such renormalization is also seen by the Bogoliubov-de Gennes equation with an impurity, where the strong correlation is treated by a Gutzwiller mean-field theory with local Gutzwiller factors and local chemical potentials. Namely, the delta-function potential is effectively weakened and broadened. We emphasize the importance of including the local chemical potential, which is paid little attention to in the literature, by physical consideration of the doping dependence of a local hole density. We also investigate effect of smooth impurity potential variation; the strong correlation yields anticorrelation between the gap energy and the coherence peak height simultaneously with large gap distribution, which is consistent with the experiments.

cond-mat.str-el↗

arXiv2008

Impurity Scattering Effects in STM Studies of High-T_c Superconductors

Recent STM measurements have observed many inhomogeneous patterns of the local density of states on the surface of high-T_c cuprates. As a first step to study such disordered strong correlated systems, we use the BdG equation for the t-t'-t"-J model with an impurity. The impurity is taken into account by a local potential or local variation of the hopping/exchange terms. Strong correlation is treated by a Gutzwiller mean-field theory with local Gutzwiller factors and local chemical potentials. It turned out that the potential impurity scattering is greatly suppressed, while the local variation of hoppings/exchanges is enhanced.

cond-mat.str-el↗

arXiv2008

The cluster glass state in the two-dimensional extended t-J model

The recent observation of an electronic cluster glass state composed of random domains with unidirectional modulation of charge density and/or spin density on Bi_{2}Sr_{2}CaCu_{2}O_{8+δ} reinvigorates the debate of existence of competing interactions and their importance in high temperature superconductivity. By using a variational approach, here we show that the presence of the cluster glass state is actually an inherent nature of the model based on the antiferromagnetic interaction (J) only, i.e. the well known t-J model. There is no need yet to introduce a competing interaction to understand the existence of the cluster glass state. The long-range pairing correlation is not much influenced by the disorder in the glass state which also has nodes and linear density of states. In the antinodal region, the spectral weight is almost completely suppressed. The modulation also produces subgap structures inside the "coherent" peaks of the local density of states.

cond-mat.supr-con↗

arXiv2008

Grand canonical Gutzwiller approximation for magnetic inhomogeneous systems

The Gutzwiller approximation (GA) for Gutzwiller-projected grand canonical wave functions with fugacity factors is investigated in detail. Our systems in general contain inhomogeneity and local magnetic moments. In deriving renormalization formulae, we also derive or estimate terms of higher powers of intersite contractions neglected in the conventional GA. We examine several different constraints, i.e., local/global spin-dependent/independent particle-number conservation. Out of the four, the local spin-dependent constraint seems the most promising at present. An improved GA derived from it agrees with the variational Monte Carlo method better than the conventional GA does. The corrections to the conventional GA can be interpreted as two-site correlation including the phase difference of configurations. Furthermore, projected quasi-particle excited states are orthogonal to each other within the GA. Using these states, spectral weights are calculated. We show that asymmetry between electron addition and removal spectra can appear by taking into account the higher powers of the intersite contractions in the case of the d-wave superconductors and the Fermi sea; the addition is smaller than the removal. However, the asymmetry is quite weak especially near the Fermi level. In contrast, projected s-wave superconductors can have the opposite asymmetry (addition larger than removal) especially near the Fermi level. In addition, formulae from the other three constraints are also derived, which may be useful depending on purposes.

cond-mat.str-el↗

arXiv2005

Particle number renormalization in almost half filled Mott Hubbard superconductors

The effects of the Gutzwiller projection on a BCS wave function with varying particle number are considered. We show that a fugacity factor has to be introduced in these wave functions when they are Gutzwiller projected, and derive an expression for this factor within the Gutzwiller approximation. We examine the effects of the projection operator on BCS wave functions by calculating the average number of particles before and after projection. We also calculate particle number fluctuations in a projected BCS state. Finally, we point out the differences between projecting BCS wave functions in the canonical and grand canonical schemes, and discuss the relevance of our results for variational Monte Carlo studies.

cond-mat.supr-con↗

arXiv2005

Vanishing Neel Ordering of SU(n) Heisenberg Model in Three Dimensions

The SU(n) Heisenberg model represented by exchange operators is studied by means of high-temperature series expansion in three dimensions, where n is an arbitrary positive integer. The spin-spin correlation function and its Fourier transform S(q) is derived up to O[(βJ)^{10}] with (βJ) being the nearest-neighbor antiferromagnetic exchange in units of temperature. The temperature dependence of S(q) and next-nearest-neighbor spin-spin correlation in the large n cases show that dominant correlation deviates from q=(π,π,π) at low temperature, which is qualitatively similar to that of this model in one dimension. The Neel temperature of SU(2) case is precisely estimated by analyzing the divergence of S(π,π,π). Then, we generalize n of SU(n) to a continuous variable and gradually increases from n=2. We conclude that the Neel ordering disappears for n>2.

cond-mat.str-el↗

arXiv2004

Thermodynamic properties of ferromagnetic mixed-spin chain systems

Using a combination of high-temperature series expansion, exact diagonalization and quantum Monte Carlo, we perform a complementary analysis of the thermodynamic properties of quasi-one-dimensional mixed-spin systems with alternating magnetic moments. In addition to explicit series expansions for small spin quantum numbers, we present an expansion that allows a direct evaluation of the series coefficients as a function of spin quantum numbers. Due to the presence of excitations of both acoustic and optical nature, the specific heat of a mixed-spin chain displays a double-peak-like structure, which is more pronounced for ferromagnetic than for antiferromagnetic intra-chain exchange. We link these results to an analytically solvable half-classical limit. Finally, we extend our series expansion to incorporate the single-ion anisotropies relevant for the molecular mixed-spin ferromagnetic chain material MnNi(NO$_{2}$)$_{4}$(ethylenediamine)$_{2}$, with alternating spins of magnitude 5/2 and 1. Including a weak inter-chain coupling, we show that the observed susceptibility allows for an excellent fit, and the extraction of microscopic exchange parameters.

cond-mat.str-el↗

arXiv2002

A New Method of the High Temperature Series Expansion

We formulate a new method of performing high-temperature series expansions for the spin-half Heisenberg model or, more generally, for SU($n$) Heisenberg model with arbitrary $n$. The new method is a novel extension of the well-established finite cluster method. Our method emphasizes hidden combinatorial aspects of the high-temperature series expansion, and solves the long-standing problem of how to efficiently calculate correlation functions of operators acting at widely separated sites. Series coefficients are expressed in terms of cumulants, which are shown to have the property that all deviations from the lowest-order nonzero cumulant can be expressed in terms of a particular kind of moment expansion. These ``quasi-moments'' can be written in terms of corresponding ``quasi-cumulants'', which enable us to calculate higher-order terms in the high-temperature series expansion. We also present a new technique for obtaining the low-order contributions to specific heat from finite clusters.

cond-mat.stat-mech↗

arXiv2002

Variational perturbation approach to the Coulomb electron gas

The efficiency of the variational perturbation theory [Phys. Rev. C {\bf 62}, 045503 (2000)] formulated recently for many-particle systems is examined by calculating the ground state correlation energy of the 3D electron gas with the Coulomb interaction. The perturbation beyond a variational result can be carried out systematically by the modified Wick's theorem which defines a contraction rule about the renormalized perturbation. Utilizing the theorem, variational ring diagrams of the electron gas are summed up. As a result, the correlation energy is found to be much closer to the result of the Green's function Monte Carlo calculation than that of the conventional ring approximation is.

cond-mat.str-el↗

arXiv2001

High Temperature Expansion for the SU(n) Heisenberg Model in One Dimension

Thermodynamic properties of the SU($n$) Heisenberg model in one dimension is studied by means of high-temperature expansion for arbitrary $n$. The specific heat up to $O[(βJ)^{23}]$ and the correlation function up to $O[(βJ)^{18}]$ are derived with $βJ$ being the antiferromagnetic exchange in units of temperature. It is found for $n>2$ that the specific heat shows a shoulder in the high-temperature side of a peak. The origin of this structure is clarified by deriving the temperature dependence of the correlation function. With decreasing temperature, the short-range correlation with two-site periodicity develops first, and then another correlation with $n$-site periodicity at lower temperature. This behavior is in contrast to that of the inverse square interaction model, where the specific heat shows a single peak according to the exact solution. Our algorithm has an advantage that neither computational time nor memory depends on the multiplicity $n$ per site; the series coefficients are obtained as explicit functions of $n$.

cond-mat.str-el↗

arXiv1998

Fluctuation Effects on the Quadrupolar Ordering in Magnetic Field

Effects of magnetic field on the quadrupolar ordering are investigated with inclusion of fluctuation of order parameters. For the simplest model with the nearest-neighbor quadrupolar interaction, the transition temperature and the specific heat are derived by the use of the recently proposed effective medium theory. It is shown that magnetic field H has two competing effects on the quadrupolar ordering; one is to encourage the ordering by suppressing the fluctuation among different components of order parameters, and the other is to block the ordering as in antiferromagnets. The former is found to be of order H^2 and the latter of order H^4. Hence the fluctuation is suppressed for weak fields, and the transition temperature increases with magnetic field. The fluctuation effect is so strong that the entropy released at the quadrupolar ordering is only about half of the full value ln 4 even without the Kondo effect.

cond-mat.str-el↗

arXiv1997

Dynamical Effective Medium Theory for Quantum Spins and Multipoles

A dynamical effective medium theory is presented for quantum spins and higher multipoles such as quadrupole moments. The theory is a generalization of the spherical model approximation for the Ising model, and is accurate up to O(1/z_n) where z_n is the number of interacting neighbors. The polarization function is optimized under the condition that it be diagonal in site indices. With use of auxiliary fields and path integrals, the theory is flexibly applied to quantum spins and higher multipoles with many interacting neighbors. A Kondo-type screening of each spin is proposed for systems with extreme quantum fluctuations but without conduction electrons.

cond-mat↗