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

Regular Article
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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.


Two-electron reduced density matrix N-representability conditions Strong electron correlation Hubbard models 



D.A.M. gratefully acknowledges the NSF, the ARO, and the Keck Foundation for their generous support. The authors express their gratitude to Dr. Jonathan J. Foley for assistance with the configuration interaction calculations.


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© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  1. 1.Department of Chemistry and The James Franck InstituteThe University of ChicagoChicagoUSA

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