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arXiv · 1307.1002

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

Brecht Verstichel·Ward Poelmans·Stijn De Baerdemacker·Sebastian Wouters·Dimitri Van Neck
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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 $6\times6$ 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 $2\times2$ and $3\times3$ 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 $6\times6$ 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.

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Brecht Verstichel, Ward Poelmans, Stijn De Baerdemacker, Sebastian Wouters, Dimitri Van Neck. 2013-07-03. Variational optimization of the 2DM: approaching three-index accuracy using extended cluster constraints. https://doi.org/10.1140/epjb/e2014-40788-x

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