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Register a new userStatic correlation and electron localization in molecular dimers from the self-consistent RPA and GW approximation
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We investigate static correlation and delocalization errors in the self-consistent GW and random-phase approximation (RPA) by studying molecular dissociation of the H_2 and LiH molecules. Although both approximations contain topologically identical diagrams, the non-locality and frequency dependence of the GW self-energy crucially influence the different energy contributions to the total energy as compared to the use of a static local potential in the RPA. The latter leads to significantly larger correlation energies which allow for a better description of static correlation at intermediate bond distances. The substantial error found in GW is further analyzed by comparing spin-restricted and spin-unrestricted calculations. At large but finite nuclear separation their difference gives an estimate of the so-called fractional spin error normally determined only in the dissociation limit. Furthermore, a calculation of the dipole moment of the LiH molecule at dissociation reveals a large delocalization error in GW making the fractional charge error comparable to the RPA. The analyses are supplemented by explicit formulae for the GW Greens function and total energy of a simplified two-level model providing additional insights into the dissociation limit.
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In many-body perturbation theory (MBPT) the self-energy Sigma=iGWGamma plays the key role since it contains all the many body effects of the system. The exact self-energy is not known; as first approximation one can set the vertex function Gamma to unity which leads to the GW approximation. The latter properly describes the high-density regime, where screening is important; in the low-density regime, instead, other approximations are proposed, such as the T matrix, which describes multiple scattering between two particles. Here we combine the two approaches. Starting from the fundamental equations of MBPT we show how one can derive the T-matrix approximation to the self-energy in a common framework with GW. This allows us to elucidate several aspects of this formulation, including the origin of, and link between, the electron-hole and the particle-particle T matrix, the derivation of a screened T matrix, and the conversion of the T matrix into a vertex correction. The exactly solvable Hubbard molecule is used for illustration.
Quantum embedding approaches involve the self-consistent optimization of a local fragment of a strongly correlated system, entangled with the wider environment. The `energy-weighted density matrix embedding theory (EwDMET) was established recently as a way to systematically control the resolution of the fragment-environment coupling, and allow for true quantum fluctuations over this boundary to be self-consistently optimized within a fully static framework. In this work, we reformulate the algorithm to ensure that EwDMET can be considered equivalent to an optimal and rigorous truncation of the self-consistent dynamics of dynamical mean-field theory (DMFT). A practical limitation of these quantum embedding approaches is often a numerical fitting of a self-consistent object defining the quantum effects. However, we show here that in this formulation, all numerical fitting steps can be entirely circumvented, via an effective Dyson equation in the space of truncated dynamics. This provides a robust and analytic self-consistency for the method, and an ability to systematically and rigorously converge to DMFT from a static, wave function perspective. We demonstrate that this improved approach can solve the correlated dynamics and phase transitions of the Bethe lattice Hubbard model in infinite dimensions, as well as one- and two-dimensional Hubbard models where we clearly show the benefits of this rapidly convergent basis for correlation-driven fluctuations. This systematically truncated description of the effective dynamics of the problem also allows access to quantities such as Fermi liquid parameters and renormalized dynamics, and demonstrates a numerically efficient, systematic convergence to the zero-temperature dynamical mean-field theory limit.
We present quasiparticle (QP) energies from fully self-consistent $GW$ (sc$GW$) calculations for a set of prototypical semiconductors and insulators within the framework of the projector-augmented wave methodology. To obtain converged results, both finite basis-set corrections and $k$-point corrections are included, and a simple procedure is suggested to deal with the singularity of the Coulomb kernel in the long-wavelength limit, the so called head correction. It is shown that the inclusion of the head corrections in the sc$GW$ calculations is critical to obtain accurate QP energies with a reasonable $k$-point set. We first validate our implementation by presenting detailed results for the selected case of diamond, and then we discuss the converged QP energies, in particular the band gaps, for a set of gapped compounds and compare them to single-shot $G_0W_0$, QP self-consistent $GW$, and previously available sc$GW$ results as well as experimental results.
The emph{GW} approximation takes into account electrostatic self-interaction contained in the Hartree potential through the exchange potential. However, it has been known for a long time that the approximation contains self-screening error as evident in the case of the hydrogen atom. When applied to the hydrogen atom, the emph{GW} approximation does not yield the exact result for the electron removal spectra because of the presence of self-screening: the hole left behind is erroneously screened by the only electron in the system which is no longer present. We present a scheme to take into account self-screening and show that the removal of self-screening is equivalent to including exchange diagrams, as far as self-screening is concerned. The scheme is tested on a model hydrogen dimer and it is shown that the scheme yields the exact result to second order in $(U_{0}-U_{1})/2t$ where $U_{0}$ and $U_{1}$ are respectively the onsite and offsite Hubbard interaction parameters and $t$ the hopping parameter.
The self-consistent harmonic approximation is extended in order to account for the existence of Klein factors in bosonized Hamiltonians. This is important for the study of finite systems where Klein factors cannot be ignored a priori. As a test we apply the method to interacting spinless fermions with modulated hopping. We calculate the finite-size corrections to the energy gap and the Drude weight and compare our results with the exact solution for special values of the model parameters.
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