International Workshop on 'New challenges in Reduced Density Matrix Functional Theory: Symmetries, time-evolution and entanglement'
The time-dependent two-particle reduced density matrix methodStefan Donsa
Technical University Wien, Austria
Coauthor(s) : F. Lackner, T. Sato, K. Ishikawa, Joachim Burgdörfer, I. Brezinova
 University of Tokyo, Japan
Describing time-dependent many-body systems where correlation effects play an important role remains a major theoretical challenge. The full solution of the full N-body Schrödinger equation is prohibitive for large systems due to the exponential scaling with the number of particles. Frequently employed approaches to treat time-dependent many-body systems are based on effective mean-field approaches, e.g. time-dependent density functional theory, or multi-configurational methods like the multi-configurational time-dependent Hartree Fock method. While the first one makes computation of large systems feasible but is lacking the accuracy of wave-function based methods, the second approach is in principle exact but the exponential scaling with the number of particles limits its application to small system sizes. To bridge the gap between those two descriptions we developed the time-dependent two-particle reduced density matrix (TD-2RDM) method [1, 2], which allows to treat correlations up to the two-particle level exactly and circumvents the exponential scaling of multi-configurational methods. The TD-2RDM method is based on a contraction consistent reconstruction of the three-particle reduced density matrix, as required for the proper closure of the equations of motion for the TD-2RDM. Contraction consistency and enforcing N-representability constraints are key to achieve accurate and stable propagation of correlated dynamics. We show benchmark results for atoms in strong laser fields  and the non-equilibrium dynamics in Hubbard clusters. We will highlight the importance of two-particle correlations and discuss future developments and applications of the method.
 F. Lackner et al., Phys. Rev. A 91 023412 (2015).
 F. Lackner et al., Phys. Rev. A 95 033414 (2017).