Related papers: $GW$ vertex corrected calculations for molecular s…
In this paper a hybridized weak Galerkin (HWG) finite element method for solving the Stokes equations in the primary velocity-pressure formulation is introduced. The WG method uses weak functions and their weak derivatives which are defined…
We present a scalable implementation of the $GW$ approximation using Gaussian atomic orbitals to study the valence and core ionization spectroscopies of molecules. The implementation of the standard spectral decomposition approach to the…
We describe the following new features which significantly enhance the power of the recently developed real-space imaginary-time GW scheme (Rieger et al., Comp. Phys. Commun. 117, 211 (1999)) for the calculation of self-energies and related…
Coupled-cluster (CC) theory and Green's function many-body perturbation theory (MBPT) have long evolved as distinct yet complementary frameworks for describing electronic correlation. While CC methods employ exponential wavefunction…
On the basis of the self-consistent calculation scheme for the electron self-energy with the use of the three-point vertex function always satisfying the Ward identity, we find that the obtained quasiparticle dispersion in the normal state…
We introduce a systematic hierarchy of one-body Green's function methods derived from the $GW$ approximation, constructed by progressively reducing the dynamical content of the self-energy. Starting from the fully dynamical Dyson…
We present a numerical integration scheme for evaluating the convolution of a Green's function with a screened Coulomb potential on the real axis in the GW approximation of the self energy. Our scheme takes the zero broadening limit in…
The sine(sinh)-Gordon hierarchy of integrable Hamiltonian systems is described in detail, and all dynamic variables are expressed in terms of the $\wp$-functions that uniformize the associated spectral curve. Quasi-periodic solutions to the…
The magnon Hedin's equations are derived via the Schwinger functional derivative technique, and the resulting self-consistent Green's function method is used to calculate ground state spin patterns and magnetic structure factors for…
This paper introduces an auto-stabilized weak Galerkin (WG) finite element method for biharmonic equations with built-in stabilizers. Unlike existing stabilizer-free WG methods limited to convex elements in finite element partitions, our…
$GW$ is an accurate method for computing electron addition and removal energies of molecules and solids. In a conventional $GW$ implementation, however, its computational cost is $O(N^4)$ in the system size $N$, which prohibits its…
In a recent paper [Phys. Rev. B 90, 115134 (2014)] we put forward a diagrammatic expansion for the self-energy which guarantees the positivity of the spectral function. In this work we extend the theory to the density response function. We…
Dendrites have voltage-gated ion channels which aid in production of action potentials. Thus dendrites are not just passive conductors of information, but actively act on the incoming input. Here we assume Hodgkin-Huxley formulations of…
We consider a scalar Hamiltonian nonlinear wave equation formulated on networks; this is a non standard problem because these domains are not locally homeomorphic to any subset of the Euclidean space. More precisely, we assume each edge to…
We present a tight-binding based GW approach for the calculation of quasiparticle energy levels in confined systems such as molecules. Key quantities in the GW formalism like the microscopic dielectric function or the screened Coulomb…
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…
The energy gap of correlated Hubbard clusters is well studied for one-dimensional systems using analytical methods and density-matrix-renormalization-group (DMRG) simulations. Beyond 1D, however, exact results are available only for small…
The Non-Equilibrium Green's Function (NEGF) method combined with ab initio calculations has been widely used to study charge transport in molecular junctions. However, the significant computational demands of high-resolution calculations…
A new weak Galerkin (WG) finite element method for solving the second-order elliptic problems on polygonal meshes by using polynomials of boundary continuity is introduced and analyzed. The WG method is utilizing weak functions and their…
The use of Green's function in quantum many-body theory often leads to nonlinear eigenvalue problems, as Green's function needs to be defined in energy domain. The $GW$ approximation method is one of the typical examples. In this article,…