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

TL;DR

This paper develops a variational approach to optimize the two-dimensional Hubbard model's reduced density matrix, using extended cluster constraints to approximate three-index accuracy efficiently on large lattices.

Contribution

It introduces new extended cluster constraints that incorporate open-system effects, enabling near three-index accuracy with reduced computational cost.

Findings

Extended cluster constraints recover much of the three-index accuracy.

Demonstrated feasibility on a 6x6 lattice.

Achieved high accuracy with lower computational expense.

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.