Comparison of one-dimensional and quasi-one-dimensional Hubbard models from the variational two-electron reduced-density-matrix method
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- Rubin, N.C. & Mazziotti, D.A. Theor Chem Acc (2014) 133: 1492. doi:10.1007/s00214-014-1492-7
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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-one-dimensional (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.