Kinematic mechanism of the modulation of the spectral intensity in the spatially uniform system of Hubbard fermions

Using the exact representation of the Green’s function constructed in terms of the Hubbard operators, it has been shown that the kinematic interaction that induces the spin-fluctuation processes in the spatially uniform system of Hubbard fermions leads to significant variations in the spectral intensity A(k, ω) in the Brillouin zone. As a result, the modulation of A(k, ω) appears in the Fermi contour. The sign of the hopping integral within the first coordination sphere is determined by the contour section, where A(k, ω) decreases according to the angle-resolved photoemission spectroscopy data.     

Metal-insulator transition in perovskite oxides: A low-temperature perspective

A review is presented of recent experimental results of low temperature studies of composition driven metal-insulator transition in perovskite oxides of the ABO₃ class. The evolution of physical properties like conductivity, tunnelling, density of states and magnetoconductivity has been studied at low temperatures (T < 10 K) because composition is varied so that the sample goes from the metallic state to the critical region through a weakly localized region. The results show an interesting interplay of disorder and correlation effects. Special attention has been paid to the critical region which is marked by very low conductivity and dσ/dT>0. In this region the following important observations emerge. (1) It is possible to have a metallic state [σ(T = 0) = σ ₀ ≠ 0] with σ ₀/σ _Mott ? 1 and dσ/dT > 0. (2) At T < 2 K the conductivity follows a power law σ ～T^ν , where the exponent can be related to the finite frequency response of a zero temperature phase transition. (3) The Coulomb interaction plays a major role and evidence from tunnelling experiments suggests that a gap in the density of states at the Fermi level opens up continuously as the critical region is approached from the metallic side. (4) The magnetoconductivity is relatively smaller in the metallic and the weakly localized region (except the hole-doped LaMnO₃ and related systems) but becomes very large at the critical region.     

Ferromagnetism in the Hubbard model

Whether spin-independent Coulomb interaction can be the origin of a realistic ferromagnetism in an itinerant electron system has been an open problem for a long time. Here we study a class of Hubbard models on decorated lattices, which have a special property that the corresponding single-electron Schrödinger equation hasN _d-fold degenerate ground states. The degeneracyN _d is proportional to the total number of sites ||. We prove that the ground states of the models exhibit ferromagnetism when the electron filling factor is not more than and sufficiently close to=N _d/(2||), and paramagnetism when the filling factor is sufficiently small. An important feature of the present work is that it provides examples of three dimensional itinerant electron systems which are proved to exhibit ferromagnetism in a finite range of the electron filling factor.     

Theoretical study of the stereodynamics for the reaction F+HBr

The vector correlation between products and reagents for exothermic reaction F + HBr → HF + Br has been studied using a quasi-classical trajectory (QCT) method on the latest extended Lond–Eyring–Polanyi–Sato (LEPS) potential energy surface at three collision energies of 0.1 eV, 0.2 eV and 0.3 eV. Four polarization- dependent generalized differential cross-sections (2π/σ)(dσ₀₀/dω _t ), (2π/σ)(dσ₂₀/dω _t ), (2π/σ)(dσ₂₂₊/dω _t ), (2π/σ)(dσ_21?/dω _t ) have been presented in the centre of mass frame, respectively. The distribution of dihedral angle P(φ _r ), the distribution of angle between k and j ′ , P(θ _r ), are calculated. Both the influence of the collision energy and the influence of the reagent rotation on the product polarization have been studied in the present work, and the results indicate that the product rotational angular momentum j ′ is not only aligned, but also oriented along the direction perpendicular to the scattering plane. The orientation of the HF product rotational angular momentum vector j ′ depends very sensitively on the reagent rotation and also effected by the collision energy.     

Flow to strong coupling in the two-dimensional Hubbard model

We extend the analysis of the renormalization group flow in the two-dimensional Hubbard model close to half-filling using the recently developed temperature flow formalism. We investigate the interplay of d-density wave and Fermi surface deformation tendencies with those towards d-wave pairing and antiferromagnetism. For a ratio of next nearest to nearest neighbor hoppings, t'/t = - 0.25, and band fillings where the Fermi surface is inside the Umklapp surface, only the d-pairing susceptibility diverges at low temperatures. When the Fermi surface intersects the Umklapp surface close to the saddle points, d-wave pairing, d-density wave, antiferromagnetic and, to a weaker extent, d-wave Fermi surface deformation susceptibilities grow together when the interactions flow to strong coupling. We interpret these findings as indications for a non-trivial strongly coupled phase with short-ranged superconducting and antiferromagnetic correlations, in close analogy with the spin liquid ground state in the well-understood two-leg Hubbard ladder. Received 23 January 2002     

Variational theory for correlated lattice fermions in high dimensions

A diagrammatic approach to the evaluation of correlated variational wave functions for strongly interacting fermions is presented. Diagrammatic rules for the calculation of the one-particle density matrix and the Hubbard interaction are derived which are valid for arbitraryd-dimensional lattices. An exact evaluation of expectation values is performed in the limitd=. The wellknown Gutzwiller approximation is seen to become the exact result for the expectation value of the Hubbard Hamiltonian in terms of the Gutzwiller wave function ind=. An efficient procedure to correct the Gutzwiller approximation in finite dimensions is developed. A detailed discussion of expectation values ind= in terms of explicit antiferromagnetic wave functions is given. Thereby an approximate result for the ground state energy of the Hubbard model, obtained recently within a slave-boson approach, is recovered.     

The Fermi model in describing phase transitions initiated by pressure variation

Having analyzed the pressure dependence of volume V(σ), we demonstrate that the mechanism of the phase transition in HfO₂ corresponds to the Fermi model. This indicates that at σ = 10 GPa, the ground state of Hf ions changes. Within the Fermi model, the stiffness moduli in the phases stable at σ < 10 GPa and σ > 10 GPa are calculated. It is shown that the results obtained are in better agreement with the well-known experiment than the results obtained in the framework of the quantum chemistry model (ab initio calculations) and the Birch-Murnaghan equation of state.     

Spectral function and self-energy of the one-dimensional Hubbard model in the U →∞ limit

The interpretation of the k dependent spectral functions of the one-dimensional, infinite U Hubbard model obtained by using the factorized wave-function of Ogata and Shiba is revisited. The well defined feature which appears in addition to low energy features typical of Luttinger liquids, and which, close to the Fermi energy, can be interpreted as the shadow band resulting from 2k _F spin fluctuations, is further investigated. A calculation of the self-energy shows that, not too close to the Fermi energy, this feature corresponds to a band, i.e. to a solution of the Dyson equation ω-ε(k)-ReΣ(k,ω) = 0.     

Pseudogap and symmetry of superconducting order parameter in cuprates

The phase diagram, nature of the normal state pseudogap, type of the Fermi surface, and behavior of the superconducting gap in various cuprates are discussed in terms of a correlated state with valence bonds. The variational correlated state, which is a band analogue of the Anderson (RVB) states, is constructed using local unitary transformations. Formation of valence bonds causes attraction between holes in the d-channel and corresponding superconductivity compatible with antiferromagnetic spin order. Our calculations indicate that there is a fairly wide range of doping with antiferromagnetic order in isolated CuO₂ planes. The shape of the Fermi surface and phase transition curve are sensitive to the value and sign of the hopping interaction t′ between diagonal neighboring sites. In underdoped samples, the dielectrization of various sections of the Fermi boundary, depending on the sign of t′, gives rise to a pseudogap detected in photoemission spectra for various quasimomentum directions. In particular, in bismuth-and yttrium-based ceramics (t′>0), the transition from the normal state of overdoped samples to the pseudogap state of underdoped samples corresponds to the onset of dielectrization on the Brillouin zone boundary near k=(0,π) and transition from “large” to “small” Fermi surfaces. The hypothesis about s-wave superconductivity of La-and Nd-based ceramics has been revised: a situation is predicted when, notwithstanding the d-wave symmetry of the superconducting order parameter, the excitation energy on the Fermi surface does not vanish at all points of the phase space owing to the dielectrization of the Fermi boundary at k _x=± k _y. The model with orthorhombic distortions and two peaks on the curve of T _c versus doping is discussed in connection with experimental data for the yttrium-based ceramic. Zh. éksp. Teor. Fiz. 115, 649–674 (February 1999)     

d-symmetry superconductivity due to valence bond correlations

It is shown that d-symmetry superconductivity due to valence bond correlations is possible. Valence bond correlations are compatible with antiferromagnetic spin order. In order to explictly construct a homogeneous state with the valence bond structure in the two-dimensional Hubbard model for an arbitrary doping, we have used the variational method based on unitary local transformation. Attraction between holes in the d-channel is due to modulation of hopping by the site population in course of the valence bond formation, and corresponding parameters have been calculated variationally. An important factor for the gap width is the increase in the density of states on the Fermi level due to antiferromagnetic splitting of the band. The gap width and its ratio to the T _c are 2Δ≃0.1t and 2Δ/kT _c≃4.5−4 for U/t≃8. The correspondence between the theoretical phase diagram and experimental data is discussed. The dependence of T _c on the doping δ=|n−1| and the Fermi surface shape are highly sensitive to the weak interaction t′ leading to diagonal hoppings. In the case of t′>0 and p-doping, the peak on the curve of T _c(δ) occurs at the doping δ _opt, when the energy of the flattest part of the lower Hubbard subband crosses the Fermi level at k∼(π,0). In underdoped samples with δ<δ _opt, the anisotropic pseudogap in the normal state corresponds to the energy difference |E(π,0)−μ| between this part of the spectrum and the Fermi level. Zh. éksp. Teor. Fiz. 114, 985–1005 (September 1998)     

Electronic states near fermi level in superconductors La2 − x Sr x CuO4 by means of x-ray absorption spectra near Cu-K and La-L edges

The electronic states of La_{2? x} Sr _x CuO₄ with 0.00 ≤ x ≤ 0.20 are studied by means of X-ray absorption spectroscopy (XANES, EXAFS) near the K-edge of Cu²⁺ ion and the L-edges of La³⁺ ion. It is found that characteristic white lines occurring near L _II and L _III edges of La³⁺ ion show a slight energy shift depending on substituted Sr²⁺ ions, x and temperature. The white lines suggest that unoccupied high-density 5dπ and 5dδ bands of La³⁺ ion just above a Fermi level transform to a hybridized single band of 5dπδ at 78?K in the superconductors with x = 0.10, 0.16 and 0.20. On the other hand, the XANES spectra near the Cu-K edge including a pre-edge region do not depend on x and temperature in the region of 0.00 ≤ x ≤ 0.20. It is considered that there is no reconstruction of electronic states at the Fermi level in a Mott–Hubbard band gap between an O 2p valence band and a Cu 3d conduction band. The electronic states at the Fermi level are probably consisted of the unoccupied 5dπδ band and an empty charge-transfer 3d?⁹ L band at low temperature, bands of which occur in a band gap between a filled O 2p valence band and an unoccupied O 2p conduction band. The insulator–superconductor–metal transitions in La_{2? x} Sr _x CuO₄ are related to the 5dπδ and 3d?⁹ L bands and holes, which site at a top region of the O 2p valence band near the Fermi level produced by a substitution of La³⁺ with Sr²⁺ ions.     

Landau-Fermi liquid analysis of the 2D t-t' Hubbard model

We calculate the Landau interaction function f (k,k') for the two-dimensional t-t' Hubbard model on the square lattice using second and higher order perturbation theory. Within the Landau-Fermi liquid framework we discuss the behavior of spin and charge susceptibilities as function of the onsite interaction and band filling. In particular we analyze the role of elastic umklapp processes as driving force for the anisotropic reduction of the compressibility on parts of the Fermi surface. Received 18 March 2002 Published online 9 July 2002     

Symmetry analysis of the interplay between local moment anisotropies and propagation vectors in the borocarbides

Representational analysis is used to examine the interplay between Fermi surface nesting and local moment effects in the formation of the magnetically ordered states of the rare-earth nickel borocarbides, RNi₂B₂C. We derive compatibility tables for the propagation wavevector k, the local moment anisotropy and the ordered moment direction μ _k for materials with this tetragonal crystal structure. The magnetic structures observed in the rare-earth nickel borocarbides are discussed in this context.     

On the fermi velocity and static conductivity of epitaxial graphene

The models of the energy density of states of a metallic or semiconductor substrate, which does not further lead to divergences, have been proposed to calculate the characteristics of epitaxial graphene. The Fermi velocity of epitaxial graphene formed on a metal has been shown to be greater than that in free-standing graphene irrespective of the position of the Fermi level. On the contrary, the Fermi velocity of graphene formed on a semiconductor is lower so that the lower is the Fermi velocity, the closer is the Fermi level to the center of the band gap of the semiconductor. The zero-temperature static conductivity σ of epitaxial graphene has been calculated according to the Kubo-Greenwood formula. The quantity σ_m of undoped graphene on metal has been shown to decrease with an increase in the deviation of the Dirac point ?_D (which coincides with the Fermi level of the system) from the center of the conduction band of the substrate. In the case of the semiconductor substrate, the static conductivity σ_sc turns out to be nonzero and amounts to σ_sc = 2e ²/π?-only under the condition ?_F =?′_D, where ?′_D is the Dirac-point energy renormalized by the interaction with the substrate.     

Kinetic investigation on carbamate formation from the reaction of carbon dioxide with amino acids in homogeneous aqueous solution

The kinetics of carbamate formation from the reaction of carbon dioxide with α‐amino acids in D₂O was first investigated by means of nuclear magnetic resonance spectroscopy. Potassium carbonate was used as the CO₂ source. For each amino acid, the maximum carbamate yield, the apparent rate constant for the carbamate formation k_app, and the rate constants for the formation k₁ and the breakdown k_?1 of the carbamate were estimated. Plots of log k₁ or log k_?1 versus pK_a of amino acids indicated that the formation rate k₁ increased with the basicity (pK_a) of amino acid, while the decomposition rate k_?1 decreased. A Br?nsted β value of 0.39 was obtained from the former plot, being in good agreement with the previously reported ones (0.26–0.43). The observed negative pK_a dependence of log k_?1 (Br?nsted α = 0.34) is reasonable, because the carbamate decomposition is acid‐catalyzed and the steady‐state concentration of H⁺ should be higher for weaker basic amines. The charge (σ) and the lone‐pair energy (E_N) at the nitrogen atom of the amino group were calculated. Although log k₁ correlated with σ and E_N, log k_?1 was unrelated with both of these parameters. Considering that the carbamate formation (k₁) is not only base‐catalyzed but should also be promoted by the nucleophilicity of the amino nitrogen, its correlation with σ and E_N in addition to pK_a is rational. The irrelevance of log k_?1 to σ and E_N is not surprising, because σ and E_N are not a direct measure of [H⁺] of the solution. Copyright © 2011 John Wiley & Sons, Ltd.     

Fourier space analysis of the Yvon-Born-Green equation in the critical region

The pair correlation function implied by the Yvon-Born-Green (YBG) integral equation is analyzed in Fourier space in the critical region. For potentials of infinite range decaying like r^-d-σ the upper borderline dimensionality above which the solutions can be Ornstein-Zernike-like is d_> = 4 for σ ? 2 but d_> = 2σ for σ < 2, while for finite range potentials d_> = 4, confirming results found by real-space analysis. Although the borderline dimensionality is in agreement with expectations from lattice models and field theory, the analysis indicates that below d_> the solutions of the YBG equation cannot exhibit a physically acceptable critical regime. Moreover, it is shown that corrections to the YBG equation arising from further terms in the BBGKY hierarchy diverge at criticality even for d>d_>.     

Size-dependent energy scales in the ideal fermi gas

Abstract

The simplest model for the electronic properties of small metal particles is an ideal Fermi gas confined to a finite volume. When the confining region of size L has a regular shape such as a sphere or a cube, there are two distinct scales of energy which characterize the spectrum of eigenvalues near the Fermi energy E_F ≡ ?² k ² _f/2m. The inner scale δ ～ E_F /(k_FL)² is the mean spacing between successive energy levels, while the outer energy scale Δ ～ E_F /(k_FL) describes clustering of several levels, or shell structure. Consequences for the behaviour of thermodynamic properties are investigated. There are three regimes of temperature T: normal metallic (T > Δ), shell-metallic (δ < T < Δ) and semiconductor-like (T < δ). Finally, if the shape of a hard-walled container is allowed to vary so as to minimize the energy, it is argued that the optimal shape fluctuates between spherical and distorted as L is changed.     

Analytical representation of the density derivative of the Percus–Yevick hard-sphere radial distribution function

ABSTRACT

Explicit analytical expressions are presented for the density derivative, ?g_HS(R; ρ)/?ρ, of the Percus–Yevick approximation to the hard-sphere radial distribution function for R ≤ 6σ, where σ is the hard-sphere diameter and ρ = (N/V)σ³ is the reduced density, where N is the number of particles and V is the volume. A FORTRAN program is provided for the implementation of these for R ≤ 6σ, which includes code for the calculation of g_HS(R; ρ) itself over this range. We also present and incorporate within the program code convenient analytical expressions for the numerical extrapolation of both quantities past R = 6σ. Our expressions are numerically tested against exact results.     

The dynamics of quantum discord and entanglement of two atoms coupled to two spatially separate cavities in cavity QED

We demonstrate that a kind of highly excited state of strongly attractive Hubbard model, named of Fermi super-Tonks-Girardeau state, can be realized in the spin-1/2 Fermi optical lattice system by a sudden switch of interaction from the strongly repulsive regime to the strongly attractive regime. In contrast to the ground state of the attractive Hubbard model, such a state is the lowest scattering state with no pairing between attractive fermions. With the aid of Bethe-ansatz method, we calculate energies of both the Fermi Tonks-Girardeau gas and the Fermi super-Tonks-Girardeau state of spin-1/2 ultracold fermions and show that both energies approach to the same limit as the strength of the interaction goes to infinity. By exactly solving the quench dynamics of the Hubbard model, we demonstrate that the Fermi super-Tonks-Girardeau state can be transferred from the initial repulsive ground state very efficiently. This allows the experimental study of properties of Fermi super-Tonks-Girardeau gas in optical lattices.