Eur. Phys. J. B (2014) 87: 59
https://doi.org/10.1140/epjb/e2014-40788-x

Regular Article

Variational optimization of the 2DM: approaching three-index accuracy using extended cluster constraints

Center for Molecular Modeling, Ghent University, Technologiepark 903, 9052 Zwijnaarde, Belgium

^a e-mail: brecht.verstichel@ugent.be

Received: 23 August 2013
Received in final form: 30 November 2013
Published online: 10 March 2014

Abstract

The reduced density matrix is variationally optimized for the two-dimensional Hubbard model. Exploiting all symmetries present in the system, we have been able to study 6 × 6 lattices at various fillings and different values for the on-site repulsion, using the highly accurate but computationally expensive three-index conditions. To reduce the computational cost we study the performance of imposing the three-index constraints on local clusters of 2 × 2 and 3 × 3 sites. We subsequently derive new constraints which extend these cluster constraints to incorporate the open-system nature of a cluster on a larger lattice. The feasibility of implementing these new constraints is demonstrated by performing a proof-of-principle calculation on the 6 × 6 lattice. It is shown that a large portion of the three-index result can be recovered using these extended cluster constraints, at a fraction of the computational cost.