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Minimizing the energy of an $N$-electron system as a functional of atwo-electron reduced density matrix (2-RDM), constrained by necessary$N$-representability conditions (conditions for the 2-RDM to represent anensemble $N$-electron quantum system), yields a rigorous lower bound to theground-state energy in contrast to variational wavefunction methods. Wecharacterize the performance of two sets of approximate constraints,(2,2)-positivity (DQG) and approximate (2,3)-positivity (DQGT) conditions, atcapturing correlation in one-dimensional and quasi-one-dimensional (ladder)Hubbard models. We find that, while both the DQG and DQGT conditions captureboth the weak and strong correlation limits, the more stringent DQGT conditionsimprove the ground-state energies, the natural occupation numbers, the paircorrelation function, the effective hopping, and the connected (cumulant) partof the 2-RDM. We observe that the DQGT conditions are effective at capturingstrong electron correlation effects in both one- and quasi-one-dimensionallattices for both half filling and less-than-half filling.

Comparison of one-dimensional and quasi-one-dimensional Hubbard models from the variational two-electron reduced-density-matrix method