Particle Green Function Research Articles

Kondo Effect in Electron Tunneling through Quantum Dots - Study with Quantum Monte Carlo Method -

Based on the Quantum Monte Carlo (QMC) technique, we developed a method to calculate the tunneling conductance of the quantum dot systems for which the Kondo effect becomes important. The method computes the conductance directly from the current correlation function, and is applicable to the cases in which the calculation is not reduced to the computation of single particle Green's function. We compare the calculated conductance with experiments, and found good qualitative agreement. The temperature in experiments seems to be not low enough compared with the Kondo temperature in the mid region of the two paired Coulomb oscillation peaks. We studied the Zeeman field effect, and showed that the conductance is strongly suppressed when it has been enhanced by the Kondo effect. The conductance of an Aharonov-Bhom circuit including dots was also studied.

Occupation numbers in Self Consistent RPA

A method is proposed which allows to calculate within the SCRPA theory the occupation numbers via the single particle Green function. This scheme complies with the Hugenholtz van Hove theorem. In an application to the Lipkin model it is found that this prescription gives consistently better results than two other commonly used approximations: lowest order boson expansion and the number operator method.

Fermiology of a one-dimensional heavy-electron metal

We present a Quantum Monte Carlo (QMC) study of the 1D Kondo lattice at non-integer filling, i.e. a one-dimensional version of a heavy electron metal. For this special system the minus-sign problem turns out to be strongly reduced, which allows QMC simulations for temperatures as low as 1% of the conduction electron bandwidth. The single particle Green's function shows and intricate network of low-energy bands at low temperature, with a Fermi surface volume that comprises both c and f-electrons. As temperature increases the system evolves through two distinct crossover temperatures into a very simple band structure with one free c-electron band and a disconnected upper and lower Hubbard band for f-electrons. The f-electrons thus `drop out' of the Fermi surface volume as temperature increases.

Confined coherence and analytic properties of Green’s functions

A simple model of noninteracting electrons with a separable one-body potential is used to discuss the possible pole structure of single particle Green's functions for fermions on unphysical sheets in the complex frequency plane as a function of the system parameters. The poles in the exact Green's function can cross the imaginary axis, in contrast to recent claims that such a behaviour is unphysical. As the Green's function of the model has the same functional form as an approximate Green's function of coupled Luttinger liquids no definite conclusions concerning the concept of "confined coherence" can be drawn from the locations of the poles of this Green's function.

Temperature-dependent band structure of the Kondo insulator

We present a Qantum Monte Carlo (QMC) study of the temperature dependent dynamics of the Kondo insulator. Working at the so-called symmetrical point allows to perform minus-sign free QMC simulations and thus reach temperatures of less than 1% of the conduction electron bandwidth. Study of the temperature dependence of the single particle Green's function and dynamical spin correlation function shows a surprisingly intricate low temperature band structure and gives evidence for two characteristic temperatures, which we identify with the Kondo and coherence temperature, respectively. In particular, the data show a temperature induced metal-insulator transition at the coherence temperature.

Relativistic BBGKY Theory and Collision Integral of Generalized Boltzmann Equation in a Relativistic Magnetized Plasma**The project supported by National High-Tech ICF Committee in China, NSFC, AAAPT and APSC

Usually, only Coulomb interactions between charged particles which are independent of time are considered in BBGKY theory of a nonrelativistic plasma. In relativistic case, the induced electromagnetic forces between charged particles which are dependent on time obviously should be considered. A Lorentz-covariant generalized n-time Liouville equation for classical plasma is established. A convenient form applicable to the laboratory frame of this equation is also given. The relativistic BBGKY hierarchy is developed in which both Coulomb and electromagnetic forces between particles are included. A method for solving the relativistic pair correlation equation is given in polarization approximation. A new formula for calculating collision integral in terms of discrete particle Green functions is given. A number of generalized Boltzmann equations for relativistic plasmas are derived.

Confinement in the Coulomb Gauge Model

The Coulomb gauge model of QCD is studied with the introduction of a confining potential into the scalar part of the vector potential. Using a Green function formalism, we derive the self-energy for this model, which has both scalar and vector parts,ΣS(p) andΣV(p). A rotation of these variables leads to the so-called gap and energy equations. We then analyse the divergence structure of these equations. As this depends explicitly on the form of potential, we give as examples both the linear plus Coulomb and quadratically confining potentials. The nature of the confining single particle Green function is investigated, and shown to be divergent due to the infrared singularities caused by the confining potential. Solutions to the gap equation for the simpler case of quadratic confinement are found both semi-analytically and numerically. At finite temperatures, the coupled set of equations are solved numerically in two decoupling approximations. Although chiral symmetry is found only to be exactly restored asT→∞, the chiral condensate displays a steep drop over a somewhat small temperature range.

Spin-charge separated Luttinger liquid in arbitrary spatial dimensions

A model with a singular forward scattering amplitude for particles with opposite spins in d spatial dimensions is proposed and solved by using the bosonization transformation. This interaction potential leads to the spin-charge separation. Thermal properties at low temperature for this normal Luttinger liquid are discussed. Also, the explicit forms of the single-electron Green function and of the spectral weight function are found; they have square-root branch cuts. New fermion field operators are defined; they describe holons and spinons as the elementary excitations. Their single particle Green functions possess pseudo-particle properties. Using these operators the spin-charge separated Hamiltonian for ideal gases of holons and spinons is derived and reflects an inverse (fermionization) transformation.

Toulouse points and non-Fermi-liquid states in the mixed-valence regime of the generalized Anderson model.

We study the mixed valence regime of a generalized Anderson impurity model using the bosonization approach. This single impurity problem is defined by the $U=\infty$ Anderson model with an additional density-density interaction, as well as an explicit exchange interaction, between the impurity and conduction electrons. We find three points in the interaction parameter space at which all the correlation functions can be calculated explicitly. These points represent the mixed valence counterparts of the ususal Toulouse point for the Kondo problem, and are appropriately named the Toulouse points of the mixed valence problem. Two of the Toulouse points exhibit the strong coupling, Fermi liquid behavior. The third one shows spin-charge separation; here, the spin-spin correlation functions are Fermi-liquid-like, the charge-charge correlation functions and the single particle Green function have non-Fermi-liquid behaviors, and a pairing correlation function is enhanced compared to the Fermi liquid case. This third Toulouse point describes the novel intermediate mixed valence phase we have previously identified. In deriving these results, we emphasize the importance of keeping track of the anticommutation relation between the fermion fields when the bosonization method is applied to quantum impurity problems.

Conserving and gapless approximations for an inhomogeneous Bose gas at finite temperatures.

We derive and discuss the equations of motion for the condensate and its fluctuations for a dilute, weakly interacting Bose gas in an external potential within the self--consistent Hartree--Fock--Bogoliubov (HFB) approximation. Account is taken of the depletion of the condensate and the anomalous Bose correlations, which are important at finite temperatures. We give a critical analysis of the self-consistent HFB approximation in terms of the Hohenberg--Martin classification of approximations (conserving vs gapless) and point out that the Popov approximation to the full HFB gives a gapless single-particle spectrum at all temperatures. The Beliaev second-order approximation is discussed as the spectrum generated by functional differentiation of the HFB single--particle Green's function. We emphasize that the problem of determining the excitation spectrum of a Bose-condensed gas (homogeneous or inhomogeneous) is difficult because of the need to satisfy several different constraints.

Approximation of excitonic absorption in disordered systems using a compositional-component-weighted coherent-potential approximation.

Employing a recently developed technique of component weighted two particle Green's functions in the CPA of a binary substitutional alloy $A_cB_{1-c}$ we extend the existing theory of excitons in such media using a contact potential model for the interaction between electrons and holes to an approximation which interpolates correctly between the limits of weak and strong disorder. With our approach we are also able to treat the case where the contact interaction between carriers varies between sites of different types, thus introducing further disorder into the system. Based on this approach we study numerically how the formation of exciton bound states changes as the strengths of the contact potentials associated with either of the two site types are varied through a large range of parameter values.

Predictions for neutron scattering and photoemission experiments on CuGeO3.

Applying numerical techniques to a model recently proposed for the one dimensional spin-Peierls compound CuGeO_3, we calculate dynamical properties that can be directly compared with inelastic neutron scattering data and angle-resolved photoemission experiments. The momentum and energy dependence of the dynamical structure factor S(q,omega) are discussed, as well as the static structure factor S(q). The spectral function A(q,omega) calculated from the one particle Green's function at half-filling is shown at several values of the hole hopping amplitude t. The results have some unique features characteristic of one dimensional systems including small weight near the Fermi energy. The presence of ``shadow bands'' induced by short distance antiferromagnetic correlations is predicted to appear in ARPES experiments for CuGeO_3 and also for Sr_2CuO_3.

One- and two-particle excitations in doped Hubbard models

We present a selfconsistent strong coupling scheme to evaluate the single particle Green's function for the two dimensional Hubbard model in the doped spin density wave state. For small doping we analyze the quasiparticle properties and the optical conductivity, emphasizing the role of multi spin-wave processes.

Application of operator algebra technique to some problems in condensed matter physics

We prove that the relaxation functions in condensed matter physics can be easily calculated by the operator algebra technique in the continued fraction representation scheme. The Dyson equation for the single particle Green's function in the Hubbard model obtained in this way is identical with the one derived by Fedro and Willson in the lowest order approximation. And the cyclotron transition absorption formula obtained by this technique is identical with that of Argyres and Sigel.

Generalized kinetic theory of sticking and desorption

We describe the kinetic processes of gas particles interacting with a solid surface in terms of Green functions. A ladder approximation to the Bethe-Salpeter equation of a corresponding non-equilibrium diagrammatic representation is applied to calculate a time dependent transition probability. Restricting the formalism to diagonal elements of the particle Green functions the theory turns out to be equivalent to a treatment using a Master equation for occupation numbers of energy levels. Cutting the iteration after a finite number of steps leads to useful approximations for the sticking coefficient. As the main result we include off-diagonal elements to obtain a generalized kinetic description. Such a theory has to be applied in the case of overlapping energy levels. Dyson's equation is diagonalized including off-diagonal elements of the self-energies. A corresponding transformation of the Bethe-Salpeter equation allows for the calculation of a generalized time dependent transition probability which can be used to extract the complete kinetic time evolution. Within a simple model we calculate sticking coefficients and desorption rates.

Validity of the rigid-band picture for the t-J model.

We present an exact diagonalization study of the doping dependence of the single particle Green's function in 16, 18 and 20 site clusters of t-J model. We find evidence for rigid-band behaviour starting from the half-filled case: upon doping, the topmost states of the quasiparticle band observed in the photoemisson spectrum at half-filling cross the chemical potential and reappear as the lowermost states of the inverse photoemission spectrum. Features in the inverse photoemission spectra which are inconsistent with rigid-band behaviour are shown to originate from the nontrivial point group symmetry of the ground state with two holes, which enforces different selection rules than at half-filling. Deviations from rigid band behaviour which lead to the formation of the `large Fermi surface' in the momentum distribution occur only at energies far from the chemical potential. A Luttinger Fermi surface and a nearest neighbor hopping band do not exist.

Single particle excitations in itinerant antiferromagnets at small doping

We present a self-consistent strong coupling scheme to evaluate the single particle Green's function for the two-dimensional Hubbard model in the spin density wave state. We analyze the single quasi-hole properties including its dispersion and the spectral weight. Novel incoherent contributions to the spectral function resulting from multi-spin wave processes are discussed.

Single particle excitations in itinerant antiferromagnets at small doping

We present a selfconsistent strong coupling scheme to evaluate the single particle Green's function for the two dimensional Hubbard model in the doped spin density wave state. For small doping we analyze the quasiparticle properties including the dispersion and the quasiparticle weight. Novel incoherent contributions to the spectral function resulting from multi spin wave processes are discussed.

Magnetoconductivity of disordered two dimensional tight binding electrons in CPA

The magnetotransport properties of a tight binding model of electrons on a two dimensional square lattice with diagonal disorder and in a perpendicular magnetic field is investigated. The disorder is treated in the coherent potential approximation (CPA) and a quasiclassical solution of the Harper equation is used to calculate the one particle Green's function. Analytical expressions for the CPA vertex corrections to the magnetoconductivity are derived. Numerical results for the density of states and the diagonal magnetoconductivity are discussed. The vertex correction vanishes if the Harper band width is neglected.

Effects of antiferromagnetic order on the electronic states in the d-p model

Effects of the antiferromagnetic Néel order on the electronic states (in particular, on the so-called in-gap states) in the d-p model are investigated. The antiferromagnetic Néel order is dealt with in the mean field approximation and the self-consistent equations for the single particle Green's functions are solved numerically in the low-temperature limit within the approximation to the leading order in the 1/ N-expansion. The significance of the effects depends upon the number of doped carriers: the itinerant antiferromagnetic state is stable only in the intermediate doping region. Near the half-filling region the charge susceptibility becomes negative, which suggests that the itinerant antiferromagnetic states are unstable.