Variational determination of the two-particle reduced density matrix within the doubly occupied configuration interaction space: Exploiting translational and reflection invariance

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

JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT

IOP PUBLISHING LTD

Año: 2021 vol. 2021

1742-5468

This work incorporates translational and reflection symmetry reductions to the variational determination of the two-particle reduced density matrix (2-RDM) corresponding to the ground state of N-particle systems, within the doubly occupied configuration interaction (DOCI) space. By exploiting these symmetries within this lower-bound variational methodology it is possible to treat larger systems than those previously studied. The 2-RDM matrix elements are calculated by imposing up to four-particle N-representability constraint conditions using standard semidefinite programing algorithms. The method is applied to the one- and two-dimensional XXZ spin 1/2 model of quantum magnetism. Several observables including the energy and the spin-spin correlation functions are obtained to assess the physical content of the variationally determined 2-RDM. Comparison with quantum-Monte Carlo and matrix product state simulations shows that in most cases only requiring up to three-particle positivity conditions is enough to correctly describe the ground-state properties of these one- and two-dimensional models.