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

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• 作者：Nicholas C. Rubin (1)
  David A. Mazziotti (1)
  
• 关键词：Two ; electron reduced density matrix ; N ; representability conditions ; Strong electron correlation ; Hubbard models
• 刊名：Theoretical Chemistry Accounts: Theory, Computation, and Modeling (Theoretica Chimica Acta)
• 出版年：2014
• 出版时间：July 2014
• 年：2014
• 卷：133
• 期：7
• 全文大小：
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• 作者单位：Nicholas C. Rubin (1)
  David A. Mazziotti (1)
  
  1. Department of Chemistry and The James Franck Institute, The University of Chicago, Chicago, IL, 60637, USA
  
• ISSN：1432-2234

文摘

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.