Photoemission Spectra from Quantum Monte Carlo and Many-Body Perturbation Theory: The best of both worlds – PhemSpec

In this project we confront one of the grand challenges of materials science and condensed matter physics: the development of predictive and reliable approaches to describe and understand materials and ultimately to predict new ones of strategic technological interest. A unique source of information about electronic structure and excitations in materials is photoemission. In this project we propose to develop an original strategy for getting access to such spectra, even in situations where standard approaches fail. This will be achieved by combining in an innovative way Many-Body Perturbation Theory (MBPT) and Quantum Monte Carlo (QMC).

On the experimental side, modern synchrotron sources can provide detailed insight on photoemission spectra, thanks to their high intensity and broad photon energy range. However, the interpretation of the experimental data is far from obvious, and theory represents an essential complementary tool. In particular, so-called first-principles methods, such as Density Functional Theory and MBPT based on Green’s functions, promise to be predictive, since no adjustable parameters are involved. However, standard implementations of these methods are known to work reasonably well for weakly to moderately correlated materials, such as metals and standard semiconductors (e.g., Si or GaAs) but to fail for most strongly correlated systems, which are of paramount importance both from the scientific and technological point of view. A paradigmatic example of this kind of materials is paramagnetic NiO, which is erroneously predicted to be a metal by standard approximations. This of course sets limits to the description and prediction of metal-insulator phase transitions.
Based on our recent developments, we propose here to follow a different and original route based on expressing the PES in terms of n-body density matrices, which we refer to as the Many-body Effective Energy Theory (MEET). Preliminary results on bulk NiO give a qualitatively correct picture, however it is clear that further improvements are necessary. To achieve this we need more accurate density matrices, which we propose to obtain from QMC. The project can be divide in two main parts:

1) Implementation and calculation of the n-body density matrices in QMC and use in the MEET. This step will tell us up to which n-body density matrix we need to have accurate PES. We will first test the MEET+QMC paradigm on simple metals and standard semiconductors, and then we will attack strongly correlated systems, bulk NiO being the first target. This latter task requires the use of a multi-determinant wavefunction, which is a quite unexplored and challenging field for solids in QMC. We will hence use the very latest developments done in our groups. The ideal platform for this part is the open-source code QMCPACK, probably the most versatile and efficient QMC program for periodic solids.

2) The next step is to make the calculations of the PES more efficient, by using only effective 1-body and 2-body density matrices. This part requires novel formal developments, which will be done along two lines: i) approximate resummation of higher-order density matrices by using a proper terminating function; ii) using a model Hamiltonian that includes already some effective screening and deriving the corresponding 1- and 2-body density matrices to be used in the MEET.

It can be expected that the project will initiate further studies, such as: i) the study of phase transitions, ii) the development of better approximations to the exchange-correlation potentials of Density Functional Theory and Reduced Density-Matrix functional theory, iii) the extension of the same strategy to the calculation of other material properties, such as absorption and electron energy loss spectroscopy within QMC.