Order Self-energy Research Articles

A "moment-conserving" reformulation of GW theory.

We show how to construct an effective Hamiltonian whose dimension scales linearly with system size, and whose eigenvalues systematically approximate the excitation energies of GW theory. This is achieved by rigorously expanding the self-energy in order to exactly conserve a desired number of frequency-independent moments of the self-energy dynamics. Recasting GW in this way admits a low-scaling O[N4] approach to build and solve this Hamiltonian, with a proposal to reduce this further to O[N3]. This relies on exposing a novel recursive framework for the density response moments of the random phase approximation, where the efficient calculation of its starting point mirrors the low-scaling approaches to compute RPA correlation energies. The frequency integration of GW, which distinguishes so many different GW variants, can be performed without approximation directly in this moment representation. Furthermore, the solution to the Dyson equation can be performed exactly, avoiding analytic continuation, diagonal approximations, or iterative solutions to the quasiparticle equation, with the full-frequency spectrum obtained from the complete solution of this effective static Hamiltonian. We show how this approach converges rapidly with respect to the order of the conserved self-energy moments and is applied across the GW100 benchmark dataset to obtain accurate GW spectra in comparison to traditional implementations. We also show the ability to systematically converge all-electron full-frequency spectra and high-energy features beyond frontier excitations, as well as avoiding discontinuities in the spectrum, which afflict many other GW approaches.

Stuckelberg SUSY QED and infrared problem

We review gauge invariant [Formula: see text] supersymmetric massive U(1) gauge theory coupled to matter and Stuckelberg superfields. We focus on the leading order self-energy and vertex correction to the matter field in the massless limit of both the U(1) vector superfield and the Stuckelberg superfield. We explicitly verify that the theory is infrared divergence free in the massless limit. Hence the Stuckelberg mechanism appears to be the efficient route to handle infrared divergences seen in supersymmetric quantum electrodynamics. Since these additional particles have very small masses they can serve as dark matter candidates through “Ultralight particles” mechanism.

Friedel oscillations of one-dimensional correlated fermions from perturbation theory and density functional theory

We study the asymptotic decay of the Friedel density oscillations induced by an open boundary in a one-dimensional chain of lattice fermions with a short-range two-particle interaction. From Tomonaga-Luttinger liquid theory it is known that the decay follows a power law, with an interaction dependent exponent, which, for repulsive interactions, is larger than the noninteracting value $-1$. We first investigate if this behavior can be captured by many-body perturbation theory for either the Green function or the self-energy in lowest order in the two-particle interaction. The analytic results of the former show a logarithmic divergence indicative of the power law. One might hope that the resummation of higher order terms inherent to the Dyson equation then leads to a power law in the perturbation theory for the self-energy. However, the numerical results do not support this. Next we use density functional theory within the local-density approximation and an exchange-correlation functional derived from the exact Bethe ansatz solution of the translational invariant model. While the numerical results are consistent with power-law scaling if systems of $10^4$ or more lattice sites are considered, the extracted exponent is very close to the noninteracting value even for sizeable interactions.

Real-time Kadanoff-Baym approach to nuclear response functions

Linear density response functions are calculated for symmetric nuclear matter of normal density by time-evolving two-time Green's functions in real time. Of particular interest is the effect of correlations. The system is therefore initially time-evolved with a collision term calculated in a direct Born approximation until fully correlated. An external time-dependent potential is then applied. The ensuing density fluctuations are recorded to calculate the density response. This method was previously used by Kwong and Bonitz for studying plasma oscillations in a correlated electron gas. The energy-weighted sum-rule for the response function is guaranteed by using conserving self-energy insertions as the method then generates the full vertex-functions. These can alternatively be calculated by solving a Bethe -Salpeter equation as done in works by Bozek et al. The (first order) mean field is derived from a momentum-dependent (non-local) interaction while 2nd order self-energies are calculated using a particle-hole two-body effective (or residual) interaction given by a gaussian local potential.We show results of calculations of the response function S(ɷ,q0) for q0 = 0.2, 0.4 and 0.8fm-1. Comparison is made with the nucleons being un-correlated i.e. with only the first order mean field included.We discuss the relation of our work with the Landau quasi-particle theory as applied to nuclear systems by Babu and Brown and followers.

Electron-phonon interaction and scattering in Si and Ge: Implications for phonon engineering

We report ab-initio results for electron-phonon (e-ph) coupling and display the existence of a large variation in the coupling parameter as a function of electron and phonon dispersion. This variation is observed for all phonon modes in Si and Ge, and we show this for representative cases where the initial electron states are at the band gap edges. Using these e-ph matrix elements, which include all possible phonon modes and electron bands within a relevant energy range, we evaluate the imaginary part of the electron self-energy in order to obtain the associated scattering rates. The temperature dependence is seen through calculations of the scattering rates at 0 K and 300 K. The results provide a basis for understanding the impacts of phonon scattering vs. orientation and geometry in the design of devices, and in analysis of transport phenomena. This provides an additional tool for engineering the transfer of energy from carriers to the lattice.

Two-particle correlations in a dynamic cluster approximation with continuous momentum dependence: Superconductivity in the two-dimensional Hubbard model

The DCA$^+$ algortihm was recently introduced to extend the dynamic cluster approximation (DCA) with a continuous lattice self-energy in order to achieve better convergence with cluster size. Here we extend the DCA$^+$ algorithm to the calculation of two-particle correlation functions by introducing irreducible vertex functions with continuous momentum dependence consistent with the DCA$^+$ self-energy. This enables a significantly more controlled and reliable study of phase transitions than with the DCA. We test the new method by calculating the superconducting transition temperature $T_{c}$ in the attractive Hubbard model and show that it reproduces previous high-precision determinantal quantum Monte Carlo results. We then calculate $T_c$ in the doped repulsive Hubbard model, for which previous DCA calculations could only access the weak-coupling ($U=4t$) regime for large clusters. We show that the new algorithm provides access to much larger clusters and delivers asymptotically converged results for $T_c$ for both the weak ($U=4t$) and intermediate ($U=7t$) coupling regimes, and thereby enables the accurate determination of the exact infinite cluster size result.

Second Order Selfenergy and Rate Equation in Time-Dependent Auger Processes

Second Order Selfenergy and Rate Equation in Time-Dependent Auger Processes

Anatomy of the self-energy

The general problem of representing the Greens function $G(k,z)$ in terms of self-energy in field theories lacking Wick's theorem is considered. A simple construction shows that a Dyson-like representation with a self-energy $\ensuremath{\Sigma}(k,z)$ is always possible, provided we start with a spectral representation for $G(k,z)$ for finite-sized systems and take the thermodynamic limit. The self-energy itself can then be iteratively expressed in terms of another higher order self-energy, capturing the spirit of Mori's formulation. We further discuss alternative and more general forms of $G(k,z)$ that are possible. In particular, a recent theory, by the author, of extremely correlated Fermi liquids at density $n$, for Gutzwiller projected noncanonical Fermi operators, obtains a new form of the Greens function: $G(k,z)=[(1\ensuremath{-}\frac{n}{2})+\ensuremath{\Psi}(k,z)]/[z\ensuremath{-}{\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{E}}_{k}\ensuremath{-}\ensuremath{\Phi}(k,z)],$ with a pair of self-energies $\ensuremath{\Phi}(z)$ and $\ensuremath{\Psi}(z)$. Its relationship with the Dyson form is explored. A simple version of the two-self-energies model was shown recently to successfully fit several data sets of photoemission line shapes in cuprates. We provide details of the unusual spectral line shapes that arise in this model, with the characteristic skewed shape depending upon a single parameter. The energy distribution curve (EDC) and momentum distribution curve (MDC) line shapes are shown to be skewed in opposite directions, and provide a testable prediction of the theory.

Kadanoff-Baym Approach to Entropy Production in O(N) Theory with Next-to-Leading Order Self-Energy

Abstract We investigate entropy production in the O(N) scalar theory using the Kadanoff-Baym equation. We show that one of the candidate expressions of the kinetic entropy satisfies the H-theorem in the first order of the gradient expansion with the next-to-leading-order self-energy of the 1/N expansion in the symmetric phase, and that entropy production occurs as the Green's function evolves with nonzero collision term contributions. Entropy production stops at local thermal equilibrium where the collision term contribution vanishes and the maximal entropy state is realized. We numerically examine these features of entropy production in thermalization processes in 1+1 dimensions for a couple of homogeneous cases, where the thermalization can proceed only with the off-shell effects. We find that the entropy production rate γ is larger for smaller N and is found to follow γ ∝ (1/N)ν where δ ≳ 2 at strong coupling measured in the unit of bare mass (m), ⋋= 40 m2.

Kadanoff-Baym Approach to Entropy Production inO(N) Theory with Next-to-Leading Order Self-Energy

Left in a dry. atmosphere for a while, gels become glasslike dehydrated substances. We investigated the dehydration process of some gels by adopting simultaneous time-resolved measuring method of weight and other properties. The feature during the dehydration process was different depending on the properties of the network and solvent in gel. Besides, in the DTA measurements of the dehydrated egg white gel, we observed an endothermic peak of which the intensity and peak position increased with elevating heating rate, similar to the glass transition in the non-crystalline polymers.

Entropy Production in Gluodynamics in Temporal Axial Gauge in 2+1 Dimensions

Entropy production in non-Abelian gauge theory is discussed in the limit of vanishing classical fields. Based on the Kadanoff-Baym equation with the leading order self-energy in the temporal axial gauge, the kinetic entropy is introduced and is proven to increase for a given self-energy. Numerical simulation of the Kadanoff-Baym equation for the non-Abelian gauge theory is performed in 2+1 dimensions. Starting from anisotropic distribution in momentum space, relaxation to isotropic distribution proceeds and the entropy is produced due to off-shell scattering of massive transverse polarization mode as expected from the proof of the H-theorem.

Critical behavior of density of states near Fermi energy in low-dimensional disordered metals

We study the effect of electron-electron interaction on the one-particle density of states (\emph{DOS}) $\rho^{(d)}(\epsilon,T)$ of low-dimensional disordered metals near Fermi energy within the framework of the finite temperature conventional impurity diagram technique. We consider only diffusive limit and by a geometric re-summation of the most singular first order self-energy corrections via the Dyson equation we obtain a non-divergent solution for the \emph{DOS} at low energies, while for higher energies the well-known Altshuler-Aronov corrections are recovered. At the Fermi level $\rho^{(d)}(\epsilon,T=0)\to 0$, this indicates that interacting disordered two- and quasi-one-dimensional systems are in insulating state at zero temperature. The obtained results are in good agreement with recent tunneling experiments on two-dimensional GaAs/AlGaAs heterostructures and quasi-one-dimensional doped multiwall carbon nanotubes.

IN-MEDIUM PROPERTIES OF KAONS IN A CHIRAL APPROACH

The first order self-energy corrections of the kaon in the symmetric nuclear matter are calculated from kaon-nucleon scattering matrix elements using a chiral Lagrangian within the framework of relativistic mean field approximation. It shows that the effective mass and the potential of K+ meson are identical with those of K- meson in the nuclear matter, respectively. The effective mass of the kaon in the nuclear matter decreases with the nuclear density increasing, and is not relevant to the kaon-nucleon Sigma term. The kaon-nucleus potential is positive and increases with the nuclear density. Moreover, the influence of the resonance Λ(1405) on the K--nucleus potential due to the re-scattering term is discussed. Our results indicate the K- meson could not be bound in the nuclei even if the contribution of Λ(1405) resonance is considered.

The shear viscosity of a trapped Bose-condensed gas

By obtaining Kubo formula type and using nonequilibrium Green’s functions, we calculate the shear viscosity of a trapped Bose-condensed gas below and above the Bose–Einstein condensation temperature ( T BEC). The contributions of the interactions between condensate and noncondensate atoms and between noncondensate atoms take into account to the viscous relaxation time, by evaluating second order self-energies in Beliaev approximation.

Spin-density response function in a 2D electron system under a magnetic field.

We study the spin density response function in a two-dimensional electron system under a strong perpendicular magnetic field. The theoretical framework is the extended RPA which takes into account all the second order self-energies of particle-hole propagators. Our results reproduce the data obtained by a light scattering experiment. We clarify how the extended RPA explains the empirical findings which are different even qualitatively from the RPA response. Especially the important role played by the two-particle-two-hole degrees of freedom is stressed.

The role of the Δ(1232) on the longitudinal response in the inclusive electron scattering reaction

We have performed a many-body calculation of the longitudinal nuclear ( e, e′) reaction employing a Second RPA (SRPA) formalism which contains the Δ(1232). More explicitly, our scheme contains RPA correlations as well as Hartree–Fock and second order self-energies, where an accurate evaluation of exchange terms is achieved. Using this formalism we have evaluated the longitudinal response function for 40Ca. We give final results at momentum transfers ranging from 300 up to 500 MeV/ c, obtaining a good agreement with data.

SCREENING LENGTH, DISPERSION RELATIONS AND QUARK POTENTIAL IN THERMO FIELD DYNAMICS

The screening length in a quark–gluon plasma, the dispersion relations of thermal gluon self-energy and the quark potential at high temperature are studied within the thermo field dynamics framework. By calculating the real and imaginary parts, of the gluon self-energy in one-loop order in thermo field dynamics, we obtain an expression for the screening length in a quark–gluon plasma and the dispersion relation between the real and imaginary parts. At high temperature, using photon exchange between electron-positron in a skeleton expansion and ladder approximation, the screened Coulomb potential and an expression for the screened quark potential is obtained.

Perturbative calculation of the excluded volume effect for nuclear matter in a relativistic mean-field approximation

Considering the finite volume of nucleons, a Lagrangian density is given. The first order self-energy of the nucleon and the equation of state of nuclear matter are calculated in the framework of relativistic mean-field approximation. Our results indicate the effects of the volume of nucleons are not negligible.

Theory of Spin Disorder Scattering in Heavily Mn-Doped GaAs: A Self-Consistent Approach

We have studied the theory of spin disorder scattering in Mn-doped GaAs by calculating in the weak coupling limit the charge carrier mobility limited by the critical scattering. The theory is developed by using Matsubara's temperature Green's functions and treating the exchange interaction between the carrier spins and the localized magnetic moments of the Mn-ions as a perturbation. The carrier life-time and the perturbed band energy are both calculated from the second order self-energy in a self-consistent manner in the sense that first the infinite order correction to the band energy is calculated by iterations, and then the corrected energy is inserted in the expression for the carrier life-time. Adding a contribution from the impurity scattering the total hole mobility can be estimated. Comparison of the calculated results to the experimental magnetotransport data shows good agreement. However, the measured resistivity peak near the Curie temperature is broader than the calculated one, which together with the large exchange parameter calls for an extension of the present theory to the intermediate or strong coupling cases.

Second order self-energy of the two-dimensional Hubbard model

The self-energy Σ(k; ω) of the 2D Hubbard model on the square lattice is calculated numerically in second order perturbation theory. In the limit of small frequencies the imaginary part of Σ(k; ω) is also obtained analytically. We find that at half filling ImΣ(k; ω) ∼ ω for k on the Fermi surface, with a logarithmically divergent prefactor close to the corners k = (0,±π) and (±π,0) in agreement with the numerical results.