Effective action approach to strongly correlated fermion systems

We construct a new functional for the single particle Green's function, which is a variant of the standard Baym Kadanoff functional. The stability of the stationary solutions to the new functional is directly related to aspects of the irreducible particle hole interaction through the Bethe Salpeter equation. A startling aspect of this functional is that it allows a simple and rigorous derivation of both the standard and extended dynamical mean field (DMFT) equations as stationary conditions. Though the DMFT equations were formerly obtained only in the limit of infinite lattice coordination, the new functional described in the work, presents a way of directly extending DMFT to finite dimensional systems, both on a lattice and in a continuum. Instabilities of the stationary solution at the bifurcation point of the functional, signal the appearance of a zero mode at the Mott transition which then couples t o physical quantities resulting in divergences at the transition.Comment: 9 page

Antiferromagnetism of Zn2_2VO(PO4)2_4)_2 and the dilution with Ti4+^{4+}

We report static and dynamic properties of the antiferromagnetic compound Zn$_{2}$(VO)(PO$_{4}$)$_{2}$, and the consequences of non-magnetic Ti$^{4+}$ doping at the V$^{4+}$ site. $^{31}$P nuclear magnetic resonance (NMR) spectra and spin-lattice relaxation rate ($1/T_1$) consistently show the formation of the long-range antiferromagnetic order below $T_N= 3.8-3.9$\,K. The critical exponent $\beta=0.33 \pm 0.02$ estimated from the temperature dependence of the sublattice magnetization measured by $^{31}$P NMR at 9.4\,MHz is consistent with universality classes of three-dimensional spin models. The isotropic and axial hyperfine couplings between the $^{31}$P nuclei and V$^{4+}$ spins are $A_{\rm hf}^{\rm iso} = (9221 \pm 100)$ Oe/$\mu_{\rm B}$ and $A_{\rm hf}^{\rm ax} = (1010 \pm 50)$ Oe/$\mu_{\rm B}$, respectively. Magnetic susceptibility data above 6.5\,K and heat capacity data above 4.5\,K are well described by quantum Monte-Carlo simulations for the Heisenberg model on the square lattice with $J\simeq 7.7$\,K. This value of $J$ is consistent with the values obtained from the NMR shift, $1/T_1$ and electron spin resonance (ESR) intensity analysis. Doping Zn$_2$VO(PO$_4)_2$ with non-magnetic Ti$^{4+}$ leads to a marginal increase in the $J$ value and the overall dilution of the spin lattice. In contrast to the recent \textit{ab initio} results, we find neither evidence for the monoclinic structural distortion nor signatures of the magnetic one-dimensionality for doped samples with up to 15\% of Ti$^{4+}$. The N\'eel temperature $T_{\rm N}$ decreases linearly with increasing the amount of the non-magnetic dopant.Comment: 13 pages, 12 figures, 2 table

Spin Diffusion in Double-Exchange Manganites

The theoretical study of spin diffusion in double-exchange magnets by means of dynamical mean-field theory is presented. We demonstrate that the spin-diffusion coefficient becomes independent of the Hund's coupling JH in the range of parameters JH*S >> W >> T, W being the bandwidth, relevant to colossal magnetoresistive manganites in the metallic part of their phase diagram. Our study reveals a close correspondence as well as some counterintuitive differences between the results on Bethe and hypercubic lattices. Our results are in accord with neutron scattering data and with previous theoretical work for high temperatures.Comment: 4.0 pages, 3 figures, RevTeX 4, replaced with the published versio

Microscopic Model and Phase Diagrams of the Multiferroic Perovskite Manganites

Orthorhombically distorted perovskite manganites, RMnO3 with R being a trivalent rare-earth ion, exhibit a variety of magnetic and electric phases including multiferroic (i.e. concurrently magnetic and ferroelectric) phases and fascinating magnetoelectric phenomena. We theoretically study the phase diagram of RMnO3 by constructing a microscopic spin model, which includes not only the superexchange interaction but also the single-ion anisotropy (SIA) and the Dzyaloshinsky-Moriya interaction (DMI). Analysis of this model using the Monte-Carlo method reproduces the experimental phase diagrams as functions of the R-ion radius, which contain two different multiferroic states, i.e. the ab-plane spin cycloid with ferroelectric polarization P//a and the bc-plane spin cycloid with P//c. The orthorhombic lattice distortion or the second-neighbor spin exchanges enhanced by this distortion exquisitely controls the keen competition between these two phases through tuning the SIA and DMI energies. This leads to a lattice-distortion-induced reorientation of P from a to c in agreement with the experiments. We also discuss spin structures in the A-type antiferromagnetic state, those in the cycloidal spin states, origin and nature of the sinusoidal collinear spin state, and many other issues.Comment: 23 pages, 19 figures. Recalculated results after correcting errors in the assignment of Dzyaloshinsky-Moriya vector

Self-Consistent Second Order Perturbation Theory for the Hubbard Model in Two Dimensions

We apply self-consistent second order perturbation theory (SCSOPT) with respect to the on-site repulsive interaction U to study the Hubbard model in two dimensions. We investigate single particle properties of the model over the entire doping range at zero temperature. It is shown that as doping decreases toward half-filling $\omega$-mass enhancement factor increases, while k-mass enhancement factor decreases. The increase in $\omega$-mass enhancement factor is larger than the decrease in k-mass enhancement factor, so that total-mass is larger than that in the non-interacting case. When particle number density per unit cell n is given by 0.64<n<1.0 interaction enhances anisotropy of the Fermi surface, whereas at lower densities n<0.64 interaction suppresses anisotropy of it. Due to the decrease in k-mass enhancement factor the density of states (DOS) at the Fermi level is suppressed. It is possible to understand the results within the framework of the weak coupling Fermi liquid theory.Comment: 8 pages, 12 embedded EPS figures, to appear in J. Phys. Soc. Jpn. Vol. 68-3 (1999

Robustness of the van Hove scenario for high-Tc superconductors

The pinning of the Fermi level to the van Hove singularity and the formation of flat bands in the two-dimensional t-t' Hubbard model is investigated by the renormalization group technique. The "van-Hove" scenario of non-Fermi-liquid behavior for high-Tc compounds can take place in a broad enough range of the hole concentrations. The results are in qualitative agreement with the recent ARPES data on La2CuO4.Comment: 4 pages, LaTeX, 3 figure

Optical spectra of the heavy fermion uniaxial ferromagnet UGe2_2

We report a detailed study of UGe$_{2}$ single crystals using infrared reflectivity and spectroscopic ellipsometry. The optical conductivity suggests the presence of a low frequency interband transition and a narrow free-carrier response with strong frequency dependence of the scattering rate and effective mass. We observe sharp changes in the low frequency mass and scattering rate below the upper ferromagnetic transition $T_C = 53 K$. The characteristic changes are exhibited most strongly at an energy scale of around 12 meV (100 cm$^{-1}$). They recover their unrenormalized value above $T_C$ and for $\omega >$ 40 meV. In contrast no sign of an anomaly is seen at the lower transition temperature of unknown nature $T_x \sim$ 30 K, observed in transport and thermodynamic experiments. In the ferromagnetic state we find signatures of a strong coupling to the longitudinal magnetic excitations that have been proposed to mediate unconventional superconductivity in this compound

3D Spinodal Decomposition in the Inertial Regime

We simulate late-stage coarsening of a 3D symmetric binary fluid using a lattice Boltzmann method. With reduced lengths and times l and t respectively (scales set by viscosity, density and surface tension) our data sets cover 1 < l 100 we find clear evidence of Furukawa's inertial scaling (l ~ t^{2/3}), although the crossover from the viscous regime (l ~ t) is very broad. Though it cannot be ruled out, we find no indication that Re is self-limiting (l ~ t^{1/2}) as proposed by M. Grant and K. R. Elder [Phys. Rev. Lett. 82, 14 (1999)].Comment: 4 pages, 3 eps figures, RevTex, minor changes to bring in line with published version. Mobility values added to Table

Kondo lattice model at half-filling

The single- and two-channel Kondo lattice model consisting of localized spins interacting antiferromagnetically with the itinerent electrons, are studied using dynamical mean field theory. As an impurity solver for the effective single impurity Anderson model we used the exact diagonalization (ED) method. Using ED allowed us to perform calculations for low temperatures and couplings of arbitrary large strength. Our results for the single-channel case confirm and extend the recent investigations. In the two-channel case we find a symmetry breaking phase transition with increasing coupling strength.Comment: 11 pages, 5 figure