Single Particle Self Research Articles

Strongly correlated multi-impurity models: The crossover from a single-impurity problem to lattice models

We present a mapping of correlated multi-impurity Anderson models to a cluster model coupled to a number of effective conduction bands capturing its essential low-energy physics. The major ingredient is the complex single-particle self energy matrix of the uncorrelated problem that encodes the influence to the host conduction band onto the dynamics of a set of correlated orbitals. While the real part of the self-energy matrix generates an effective hopping between the cluster orbitals, the imaginary part determines the coupling to the effective conduction bands in the mapped model. The rank of the imaginary part determines the number of independent screening channels of the problem, and allows the replacement of the phenomenological exhaustion criterion by a rigorous mathematical statement. This rank provides a distinction between multi-impurity models of first kind and of second kind. For the latter, there are insufficient screening channels available, so that a singlet ground state must be driven by the inter-cluster spin correlations. This classification provides a fundamental answer to the question of why ferromagnetic correlations between local moments are irrelevant for the spin compensated ground state in dilute impurity models, whereas they compete with the Kondo-scale in dense impurity arrays, without evoking a spin density wave. The low-temperature physics of three examples taken from the literature are deduced from the analytic structure of the mapped model, demonstrating the potential power of this approach. NRG calculations are presented for up to five site cluster. We investigate the appearance of frustration induced non-Fermi liquid fixed points in the trimer, and demonstrate the existence of several critical points of KT type at which ferromagnetic correlations suppress the screening of an additional effective spin-$1/2$ degree of freedom.

Fluctuation diagnostics of the finite-temperature quasi-antiferromagnetic regime of the two-dimensional Hubbard model

We study the finite temperature Fermi-liquid to non-Fermi-liquid crossover in the 2D Hubbard model for a range of dopings using the self-consistent ladder dual fermion method. We consider relatively high temperatures where we identify a suppression of the density of states near the Fermi level caused by a quasi-antiferromagnetic behaviour that is itself characterized by a long, but finite, correlation length scale. We perform fluctuation diagnostics to decompose the single-particle self energy into scattering $q$-vector and bosonic frequency contributions. Within this framework we find that the key contributions to the single-particle self energy that give non-Fermi-liquid character, even at weak coupling, are caused by relatively sharp $q=(\pi,\pi)$ spin fluctuations, while the decomposition in the bosonic frequency channel shows a complicated dependence on the relative strengths of zero, positive and negative frequency contributions. Finally, variation in density suggests that the tendency towards non-Fermi-liquid behavior is not substantially different for electron or hole doped systems.

Establishing conservation laws in pair-correlated many-body theories:T-matrix approaches

We address conservation laws associated with current, momentum and energy and show how they can be satisfied within many body theories which focus on pair correlations. Of interest are two well known t-matrix theories which represent many body theories which incorporate pairing in the normal state. The first of these is associated with Nozieres Schmitt-Rink theory, while the second involves the t-matrix of a BCS-Leggett like state as identified by Kadanoff and Martin. T-matrix theories begin with an ansatz for the single particle self energy and are to be distinguished from $\Phi$-derivable theories which introduce an ansatz for a particular contribution to the thermodynamical potential. Conservation laws are equivalent to Ward identities which we address in some detail here. Although $\Phi$-derivable theories are often referred to as "conserving theories", a consequence of this work is the demonstration that these two t-matrix approaches similarly can be made to obey all conservation laws. Moreover, simplifying approximations in $\Phi$-derivable theories, frequently lead to results which are incompatible with conservation.

Zero-density-limit extrapolation of the superfluid transition temperature in a unitary atomic Fermi gas on a lattice

The superfluid transition temperature $T_c$ of a unitary Fermi gas on a three-dimensional isotropic lattice with an attractive on-site interaction is investigated as a function of density $n$, from half filling down to $5.0\times 10^{-7}$ per unit cell, using a pairing fluctuation theory. We show that except at very low densities ($n^{1/3} <0.2$), where $T_c/E_F$ is linear in $n^{1/3}$, $T_c/E_F$ exhibits significant higher order nonlinear dependence on $n^{1/3}$. Therefore, linear extrapolation using results at intermediate densities such as in typical quantum Monte Carlo simulations leads to a significant underestimate of the zero density limit of $T_c/E_F$. Our result, $T_c/E_F=0.256$, at $n=0$ is subject to reduction from particle-hole fluctuations and incoherent single particle self energy corrections.

Internally electrodynamic particle model: Its experimental basis and its predictions

The internally electrodynamic (IED) particle model was derived based on overall experimental observations, with the IED process itself being built directly on three experimental facts, a) electric charges present with all material particles, b) an accelerated charge generates electromagnetic waves according to Maxwell's equations and Planck energy equation and c) source motion produces Doppler effect. A set of well-known basic particle equations and properties become predictable based on first principles solutions for the IED process; several key solutions achieved are outlined, including the de Broglie phase wave, de Broglie relations, Schr\"odinger equation, mass, Einstein mass-energy relation, Newton's law of gravity, single particle self interference, and electromagnetic radiation and absorption; these equations and properties have long been broadly experimentally validated or demonstrated. A specific solution also predicts the Doebner-Goldin equation which emerges to represent a form of long-sought quantum wave equation including gravity. A critical review of the key experiments is given which suggests that the IED process underlies the basic particle equations and properties not just sufficiently but also necessarily.

PAIR EXCITATIONS AND VERTEX CORRECTIONS IN FERMI FLUIDS AND THE DYNAMIC STRUCTURE FUNCTION OF TWO-DIMENSIONAL 3He

We use the equations–of–motion approach for time–dependent pair correlations in strongly interacting Fermi liquids to develop a theory of the excitation spectrum and the single–particle self energy in such systems. We present here the fully correlated equations and their approximate solutions for 3 He . Our theory has the following properties: It reduces to both, i) the "correlated" random–phase approximation (RPA) for strongly interacting fermions if the two–particle–two–hole correlations are ignored, and, ii) to the correlated Brillouin–Wigner perturbation theory for boson quantum fluids in the appropriate limit. iii) It preserves the two first energy–weighted sum rules, and systematically improves upon higher ones. iv) A familiar problem of the standard RPA is that it predicts a roton energy that lies more than a factor of two higher than what is found in experiments. A popular cure for this is to introduce an effective mass in the Lindhard function. No such ad–hoc assumption is invoked in our work. We demonstrate that the inclusion of correlated pair–excitations improves the dispersion relation significantly. Finally, a novel form of the density response function is derived that arises from vertex corrections in the proper polarization.

On the Thermodynamics of Dense Plasmas

AbstractThermodynamic functions of dense plasmas are determined in terms of the single particle self energy. The latter is expressed in terms of T‐matrices of the scattering theory. Explicit evaluations are carried out for the highly degenerate two component plasma.

On the low energy limit of reflection and sticking coefficients in atom surface scattering

The effect of long range van der Waals type potentials (∝ 1/z3) on elastic and inelastic scattering of atoms by solid surfaces is investigated. The elastic scattering is described in terms of the single particle self energy which was introduced already for the description of short range potential scattering. The case of Helium scattering is considered in particular. In this case a perturbation expansion of the self energy is possible. There are at least four important differences as compared to short range forces:1. (in agreement with earlier work of other groups) the WKB approximation leading to an energy independent sticking coefficient at low energies is valid down to energies being four orders of magnitude lower than for short range Morse type potentials.2. Below the range of validity of the WKB approximation the amplitude of the wave function in the attractive well drops to zero (as for short range forces). The simple effective range theory, however, is not applicable. The scattering length diverges logarithmically.3. The effect of scattering resonances also shows up only at energies being four orders of magnitude lower than for short range forces.4. Second order corrections to the inelastic seattering amplitude involve an energy shift which (due to the approximate energy independence of the zero order sticking coefficient) is almost logarithmically divergent at low energies. This leads to an increase of the sticking coefficient with decreasing energy.

Corrections to the goldstone expansion

A perturbation expansion of − lim β→∞ 1 β log 〈F| e −β H |F〉 results in the Goldstone series 1). A perturbation expansion of − lim β→∞ 1 β log Tr e −β H may contain corrections to that series. These corrections are discussed for a system of finite volume. It is found that (a) no corrections are obtained unless a class of diagrams is summed before application of the limit β → ∞, (b) the corrections of Luttinger and Ward 4) and of Balian, Bloch and De Dominicis 3) result from pre-summation of single particle self energies and spirals and (c) if larger classes of diagrams are pre-summed, further corrections result.