arXiv subjects

Alexander A. Rusakov

Publications and source records attributed to Alexander A. Rusakov.

6 recordsLinked to original sources

arXiv2019

Effect of propagator renormalization on the band gap of insulating solids

We present momentum-resolved spectral functions and band gaps from bare and self-consistent second-order perturbation theory for insulating periodic solids. We establish that, for systems with large gap sizes, both bare and self-consistent perturbation theory yield reasonable gaps. However, smaller gap sizes require a self-consistent adjustment of the propagator. In contrast to results obtained within a quasiparticle formalism used on top of bare second-order perturbation theory, no unphysical behavior of the band gap is observed. Our implementation of a fully self-consistent, $Phi$-derivable, and thermodynamically consistent finite-temperature diagrammatic perturbation theory forms a framework on which embedding theories such as the dynamical mean-field theory and self-energy embedding theories can be implemented.

cond-mat.mtrl-sci↗

arXiv2018

Self-energy embedding theory (SEET) for periodic systems

We present an implementation of the self-energy embedding theory (SEET) for periodic systems and provide a fully self-consistent embedding solution for a simple realistic periodic problem - 1D crystalline hydrogen - that displays many of the features present in complex real materials. For this system, we observe a remarkable agreement between our finite temperature periodic implementation results and well established and accurate zero temperature auxiliary quantum Monte Carlo data extrapolated to thermodynamic limit. We discuss differences and similarities with other Green's function embedding methods and provide the detailed algorithmic steps crucial for highly accurate and reproducible results.

physics.chem-ph↗

arXiv2018

Chebyshev polynomial representation of imaginary time response functions

Problems of finite-temperature quantum statistical mechanics can be formulated in terms of imaginary (Euclidean) -time Green's functions and self-energies. In the context of realistic Hamiltonians, the large energy scale of the Hamiltonian (as compared to temperature) necessitates a very precise representation of these functions. In this paper, we explore the representation of Green's functions and self-energies in terms of a series of Chebyshev polynomials. We show that many operations, including convolutions, Fourier transforms, and the solution of the Dyson equation, can straightforwardly be expressed in terms of the series expansion coefficients. We then compare the accuracy of the Chebyshev representation for realistic systems with the uniform-power grid representation, which is most commonly used in this context.

cond-mat.stat-mech↗

arXiv2016

Exploring connections between statistical mechanics and Green's functions for realistic systems. Temperature dependent electronic entropy and internal energy from a self-consistent second-order Green's function

Including finite-temperature effects from the electronic degrees of freedom in electronic structure calculations of semiconductors and metals is desired; however, in practice it remains exceedingly difficult when using zero-temperature methods, since these methods require an explicit evaluation of multiple excited states in order to account for any finite-temperature effects. Using a Matsubara Green's function formalism remains a viable alternative, since in this formalism it is easier to include thermal effects and to connect the dynamic quantities such as the self-energy with static thermodynamic quantities such as the Helmholtz energy, entropy, and internal energy. However, despite the promising properties of this formalism, little is know about the multiple solutions of the non-linear equations present in the self-consistent Matsubara formalism and only a few cases involving a full Coulomb Hamiltonian were investigated in the past. Here, to shed some light onto the iterative nature of the Green's function solutions, we self-consistently evaluate the thermodynamic quantities for a one-dimensional (1D) hydrogen solid at various interatomic separations and temperatures using the self-energy approximated to second-order (GF2). At many points in the phase diagram of this system, multiple phases such as a metal and an insulator exist, and we are able to determine the most stable phase from the analysis of Helmholtz energies. Additionally, we show the evolution of the spectrum of 1D boron nitride (BN) to demonstrate that GF2 is capable of qualitatively describing the temperature effects influencing the size of the band gap.

physics.chem-ph↗

arXiv2015

Second-order Green's function perturbation theory for periodic systems

Despite recent advances, systematic quantitative treatment of the electron correlation problem in extended systems remains a formidable task. Systematically improvable Green's function methods capable of quantitatively describing weak and at least qualitatively strong correlations appear promising candidates for computational treatment of periodic systems. We present a periodic implementation of temperature-dependent self-consistent 2nd-order Green's function method (GF2), where the self-energy is evaluated in the basis of atomic orbitals. Evaluating the real-space self-energy in atomic orbitals and solving the Dyson equation in $\mathbf{k}$-space are the key components of a computationally feasible algorithm. We apply this technique to the 1D hydrogen lattice - a prototypical crystalline system with a realistic Hamiltonian. By analyzing the behavior of the spectral functions, natural occupations, and self-energies, we claim that GF2 is able to recover metallic, band insulating, and at least qualitatively Mott regimes. We observe that the iterative nature of GF2 is essential to the emergence of the metallic and Mott phases.

physics.chem-ph↗

arXiv2014

Local Hamiltonians for quantitative Green's function embedding methods

Embedding calculations that find approximate solutions to the Schrödinger equation for large molecules and realistic solids are performed commonly in a three step procedure involving (i) construction of a model system with effective interactions approximating the low energy physics of the initial realistic system, (ii) mapping the model system onto an impurity Hamiltonian, and (iii) solving the impurity problem. We have developed a novel procedure for parametrizing the impurity Hamiltonian that avoids the mathematically uncontrolled step of constructing the low energy model system. Instead, the impurity Hamiltonian is immediately parametrized to recover the self-energy of the realistic system in the limit of high frequencies or short time. The effective interactions parametrizing the fictitious impurity Hamiltonian are local to the embedded regions, and include all the non-local interactions present in the original realistic Hamiltonian in an implicit way. We show that this impurity Hamiltonian can lead to excellent total energies and self-energies that approximate the quantities of the initial realistic system very well. Moreover, we show that as long as the effective impurity Hamiltonian parametrization is designed to recover the self-energy of the initial realistic system for high frequencies, we can expect a good total energy and self-energy. Finally, we propose two practical ways of evaluating effective integrals for parametrizing impurity models.

cond-mat.str-el↗