Variational determination of the two-particle reduced density matrix within the doubly occupied configuration interaction space: exploiting translational and reflection invariance. Issue 1 (28th January 2021)

• Record Type: Journal Article
• Authors: Massaccesi, G E; Rubio-García, A; Capuzzi, P; Ríos, E; Oña, O B; Dukelsky, J; Lain, L; Torre, A; Alcoba, D R
• Is Part Of: Journal of statistical mechanics. Issue 1(2021)
• Publication Date: 2021-01-28
• Subjects: spin chains, ladders and planes -- correlation functions; Statistical mechanics -- Periodicals; Mechanics -- Statistical methods -- Periodicals; 530.1305
• DOI: 10.1088/1742-5468/abd940
• Languages: English
• ISSNs: 1742-5468

Abstract

Abstract: 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.