Determinacion Variacional De La Matriz De Densidad De Dos Electrones Correspondiente A Funciones De Onda De Numero De Precedencia Nulo: Descripcion Eficiente de sistemas Multi-Electronicos Fuertemente Correlados

A. RUBIO-GARCIA; J. DUKELSKY; G.E. MASSACCESI; E. RIOS; O.B. OÑA; A. TORRE; D.R. ALCOBA; P. CAPUZZI; L. LAIN

Buenos Aires

Jornada; Jornadas de Difusión del Departamento de Física, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires; 2019

Universidad de Buenos Aires

The variational method constitutes one of the most important procedures to approximate the elements of the second-order reduced density matrix (2-RDM) corresponding to an N-electron system. This technique requires that the 2-RDM elements satisfy certain constraints known as N-representability conditions, which guarantee the physical meaning of the approximated 2-RDM. We have recently reported [1-4] very promising results arising from a variational method imposing the so-called two- and three-positivity conditions in systems described by doubly-occupied-configuration-interaction wave functions (or zero-seniority number wave functions). It was demonstrated that most of the strong correlation is captured by this procedure in which the corresponding optimization problem is formulated as an efficient semidefinite program (SDP). In this work we present an improvement of this method which includes more stringent N-representability constraints and allows one to break the spatial and spin symmetries. The projection of the N-electron Hamiltonian onto a zero-seniority-number space leads to sparse associated matrices without requiring specific algorithms in the use of the SDP. The energies and reduced density matrices calculated by this technique have been compared with the exact values in strongly correlated many-electron systems of interest in Condensed Matter and Molecular Physics. We show that the new N-representability conditions together with the allowed symmetry breaking provide a significant improvement with respect to previous results at an affordable computational cost.[1] W. Poelmans, M. Van Raemdonck, B. Verstichel, S. De Baerdemacker, A. Torre, L. Lain, G.E. Massaccesi, D.R. Alcoba, P. Bultinck, D. Van Neck, J. Chem. Theory Comput. 11, 4064 (2015).[2] D.R. Alcoba, A. Torre, L. Lain, G.E. Massaccesi, O.B. Oña, E.M. Honoré, W. Poelmans, D. Van Neck, P. Bultinck, S. De Baerdemacker, J. Chem. Phys. 148, 024105 (2018).[3] A. Rubio-García, D.R. Alcoba, P. Capuzzi, J. Dukelsky J. Chem. Theory Comput. 14, 4183 (2018).[4] D.R. Alcoba, P. Capuzzi, A. Rubio-García, J. Dukelsky, G.E. Massaccesi, O.B. Oña, A. Torre, and L. Lain, J. Chem. Phys. 149, 194105 (2018).