Pina Romaniello

Double excitations in correlated systems: A many–body approach

A coherent approach to the description of double excitations in correlated materials is presented: We derive stringent mathematical conditions on the algebraical structure of the Bethe-Salpeter and time-dependent density functional theory kernels that avoid the occurrence of spurious and nonphysical excitations. We discuss how these conditions need to be respected at any level of approximation, including the commonly used local density and static screening approximations. We propose a correlated kernel for the Bethe-Salpeter equation, and we illustrate several aspects of our approach with numerical calculations for model molecular systems.

Unphysical and physical solutions in many-body theories: from weak to strong correlation

Many-body theory is largely based on self-consistent equations that are constructed in terms of the physical quantity of interest itself, for example the density. Therefore, the calculation of important properties such as total energies or photoemission spectra requires the solution of non-linear equations that have unphysical and physical solutions. In this work we show in which circumstances one runs into an unphysical solution, and we indicate how one can overcome this problem. Moreover, we solve the puzzle of when and why the interacting Greens function does not unambiguously determine the underlying system, given in terms of its potential, or non-interacting Greens function. Our results are general since they originate from the fundamental structure of the equations. The absorption spectrum of lithium fluoride is shown as one illustration, and observations in the literature for some widely used models are explained by our approach. Our findings apply to both the weak and strong-correlation regimes. For the strong-correlation regime we show that one cannot use the expressions that are obtained from standard perturbation theory, and we suggest a different approach that is exact in the limit of strong interaction.

Solution to the many-body problem in one point

In this work we determine the one-body Greenʼs function as solution of a set of functional integro-differential equations, which relate the one-particle Greenʼs function to its functional derivative with respect to an external potential. In the same spirit as Lani et al (2012 New J. Phys. 14 013056), we do this in a one-point model, where the equations become ordinary differential equations (DEs) and, hence, solvable with standard techniques. This allows us to analyze several aspects of these DEs as well as of standard methods for determining the one-body Greenʼs function that are important for real systems. In particular: (i) we present a strategy to determine the physical solution among the many mathematical solutions; (ii) we assess the accuracy of an approximate DE related to the +cumulant method by comparing it to the exact physical solution and to standard approximations such as ; (iii) we show that the solution of the approximate DE can be improved by combining it with a screened interaction in the random-phase approximation. (iv) We demonstrate that by iterating the Dyson equation one does not always converge to a solution and we discuss which iterative scheme is the most suitable to avoid such errors.

Optical properties of periodic systems within the current-current response framework: pitfalls and remedies

We compare the optical absorption of extended systems using the density-density and current-current linear response functions calculated within many-body perturbation theory. The two approaches are formally equivalent for a finite momentum

Photoemission spectra from reduced density matrices: The band gap in strongly correlated systems

\mathbf{q}

Towards time-dependent current-density-functional theory in the non-linear regime

of the external perturbation. At

Green Functions and Self-Consistency: Insights From the Spherium Model

\mathbf{q}=\mathbf{0}

The self-energy beyond GW: Local and nonlocal vertex corrections

, however, the equivalence is maintained only if a small

Calculation of photoelectron spectra: A mean-field-based scheme

q

Photoelectron spectra from full time dependent self-interaction correction

expansion of the density-density response function is used. Moreover, in practical calculations this equivalence can be lost if one naively extends the strategies usually employed in the density-based approach to the current-based approach. Specifically we discuss the use of a smearing parameter or of the quasiparticle lifetimes to describe the finite width of the spectral peaks and the inclusion of electron-hole interaction. In those instances we show that the incorrect definition of the velocity operator and the violation of the conductivity sum rule introduce unphysical features in the optical absorption spectra of three paradigmatic systems: silicon (semiconductor), copper (metal) and lithium fluoride (insulator). We then demonstrate how to correctly introduce lifetime effects and electron-hole interactions within the current-based approach.