Variational Determination Of The Two-Particle Reduced Density Matrix Within The Doubly Occupied Configuration Interaction Space: Exploiting Translational And Reflection Invariance

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

JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT

IOP PUBLISHING LTD

Lugar: Londres; Año: 2021 vol. 154 p. 224104 - 224104

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.