Direct Variational Determination Of Two-Particle Reduced Density Matrices Corresponding To Zero Seniority Number Wave Functions: Generalization Of The Seniority Number Concept And Breaking Of Spin And Time-Reversal Symmetries

T.R. AYALA; E.D. RIOS; D. CORVALAN; D.R. ALCOBA; G.E. MASSACCESI; O.B. OÑA; A. TORRE; L. LAIN

La Plata

Workshop; X Workshop On Novel Methods For Electronic Structure Calculations; 2023

UNIVERSIDAD NACIONAL DE LA PLATA

The variational approach is a widely used method for approximating two-particle reduced density matrices (2-RDM) corresponding to fermionic systems. In this technique, the elements of the matrices are optimized by imposing constraints that guarantee the N-representability of the found solution [1]. Recently, satisfactory results have been described in strongly correlated systems, applying the variational method under the so-called p-positivity conditions to approximate the 2-RDMs corresponding to wave functions belonging to the interaction space of doubly occupied configurations of zero seniority number [2?5]. The optimization has been carried out by means of a conventional semidefinite program (SDP). In this work, a generalization of the concept of seniority number is proposed. An improved reformulation of the method is presented, which allows the elimination of spin and time-reversal symmetry constraints, leading to the breaking of such symmetries in the found solutions. The projection of the reduced Hamiltonian of the treated system onto the space of generalized zero seniority number allows the resulting SDP to be implemented using existing algorithms and exploiting the sparse character of the associated matrix structures. Energies and density matrices of strongly correlated many-body systems are calculated, comparing the results obtained using the new technique with those obtained from exact calculations. It is shown that the breaking of the above mentioned symmetries significantly improves over previously obtained solutions at 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, and P. Van Neck, J. Chem. Theory Comput. 11, 9, 4064?4076 (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, and S. De Baerdemacker, J. Chem. Phys. 148, 024105 (2018). [3] 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). [4] A. Rubio-García, J. Dukelsky, D. R. Alcoba, P. Capuzzi, O. B. Oña, E. Ríos, A. Torre, and L. Lain, J. Chem. Phys. 151, 154104 (2019). [5] D. R. Alcoba, O. B. Oña, L. Lain, A. Torre, P. Capuzzi, G. E. Massaccesi, E. Ríos, A. Rubio-García, and J. Dukelsky, J. Chem. Phys. 154, 224104 (2021).