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

Abstract

Minimizing the energy of an N-electron system as a functional of a two-electron reduced density matrix (2-RDM), constrained by necessary N-representability conditions (conditions for the 2-RDM to represent an ensemble N-electron quantum system), yields a rigorous lower bound to the ground-state energy in contrast to variational wave function methods. We characterize the performance of two sets of approximate constraints, (2,2)-positivity (DQG) and approximate (2,3)-positivity (DQGT) conditions, at capturing correlation in one-dimensional and quasi-onedimensional (ladder) Hubbard models. We find that, while both the DQG and DQGT conditions capture both the weak and strong correlation limits, the more stringent DQGT conditions improve the ground-state energies, the natural occupation numbers, the pair correlation function, the effective hopping, and the connected (cumulant) part of the 2-RDM. We observe that the DQGT conditions are effective at capturing strong electron correlation effects in both one- and quasi-one-dimensional lattices for both half filling and less-than-half filling.