Emulation for (very) large scale PGCM computations of nuclei
TBA
-When we are interested in describing the reorganization of electronic structure induced by the interaction between radiation and matter, two objects are particularly crucial : the one-body difference density matrix and the one-body transition density matrix. The primary motivation that led us to focus on these two matrices is as follows : the first one allows us to calculate the expectation value of one-body operators between two electronic states without needing these two states directly — for example, in TD-DFT, we do not explicitly access the excited states. The second one provides us with expected values associated with transition properties— for example, if the chosen operator is the electron’s position operator, the associated quantity is the transition dipole moment, the square of which is directly proportional to the oscillator strength.
-If we had access to the exact eigenstates of the stationary Hamiltonian, we could write an exact transition operator. It is possible to demonstrate that a combination of arbitrary complexity degrees of this operator with second quantization operators allows us to write the exact expression of our two density matrices of interest.
-As TD-DFT method do not allow the formulation of such operator, writing an approximate expression for these objects involves the use of a substitution operator. This operator is inspired by the operator that generates the central equation of the “Random Phase Approximation” method. We intend to demonstrate and justify why the choice of the complexity degree of the superoperators that can be involved in writing the expression of the two density matrices is not arbitrary.
+Arbitrariness of the degree of complexity of superoperators in the EOM formulation of TD-DFT objects
+When describing the reorganization of electronic structure induced by the interaction between light and matter, two objects are particularly crucial: the one-body difference density matrix and the one-body transition density matrix. The primary motivation that led us to focus on these two matrices is as follows: the first one allows us to calculate the difference in expectation value of one-body operators between two electronic states without needing these two states explicitly. The second one provides us expectation values associated with transition properties. +If we had access to the exact eigenstates of the stationary Hamiltonian, we could write an exact transition operator. In the equation-of-motion formalism (EOM), it is possible to prove that an arbitrary number of nested commutators, called superoperators, involving this exact operator and second quantization operators allows us to write the exact expression of our two density matrices of interest. +As time-dependent density-functional theory method (TD-DFT) cannot give access to the exact transition operator, writing an approximate expression for these matrices involves the use of a substitution operator. This operator is inspired by the operator that generates the central equation of the Random Phase Approximation method. The use of superoperators in TD-DFT is enabled by the structure of its fundamental equation and its physical interpretation. Interestingly, there exists a structural and interpretational identity between the fundamental equations of TD-DFT and Bethe-Salpeter equation (BSE) methods. The development carried out with the substitution operator in TD-DFT is also applicable to BSE. +We intend to demonstrate and justify that, in this specific context, the choice of the complexity degree of the superoperators might not be arbitrary — unlike with an exact transition operator — and require a minimum degree of complexity for superoperators, in order to express the two density matrices.
+[1] Thibaud Etienne. A comprehensive, self-contained derivation of the one-body density matrices from single-reference excited-state calculation methods using the equation-of-motion formalism, arxiv repository 1811.08849v15. 2018. +[2] Andrei Ipatov, Felipe Cordova, Lo ̈ıc Joubert Doriol, and Mark E. Casida. Excited-state spin- contamination in time-dependent density-functional theory for molecules with open-shell ground states. Journal of Molecular Structure: THEOCHEM, 914(1-3):60–73, November 2009. +[3] Xavier Blase, Ivan Duchemin, and Denis Jacquemin. The Bethe–Salpeter equation in chemistry: relations with TD-DFT, applications and challenges. Chemical Society Reviews, 47(3):1022–1043, 2018.
Application of DMFT to realistic materials : the example of Ba2IrO4
Describing the behavior of strongly correlated materials from first principles remains nowadays a challenge in computational condensed matter physics. Indeed, when Coulomb interaction is of the same order of magnitude as the kinetic energy of the electrons, like in materials with open d-shells, the Kohn-Sham band structure obtained within Density Functional Theory (DFT) is often quantitatively – and even sometimes qualitatively – wrong. To take strong correlations into account, Dynamical Mean Field Theory (DMFT) has been successfully coupled with DFT, in a scheme dubbed DFT+DMFT, to treat such systems for the past 25 years [1,2].