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Effective Hamiltonians Derived from Equation-of-Motion Coupled-Cluster Wave-Functions: Theory and Application to the Hubbard and Heisenberg Hamiltonians

submitted on 22.12.2019, 00:54 and posted on 23.12.2019, 22:34 by Pavel Pokhilko, Anna I. Krylov
Effective Hamiltonians, which are commonly used for fitting experimental observables, provide a coarse-grained representation of exact many-electron states obtained in quantum chemistry calculations; however, the mapping between the two is not trivial. In this contribution, we apply Bloch’s formalism to equation-of-motion coupled-cluster (EOM-CC) wave functions to rigorously derive effective Hamiltonians in the Bloch’s and des Cloizeaux’s forms. We report the key equations and illustrate the theory by examples of systems with electronic states of covalent and ionic characters. We show that the Hubbard and Heisenberg Hamiltonians are extracted directly from the so-obtained effective Hamiltonians. By making quantitative connections between many-body states and simple models, the approach also facilitates the analysis of the correlated wave functions. Artifacts affecting the quality of electronic structure calculations such as spin contamination are also discussed.


Theoretical framework for new magnetic materials for quantum computing and information storage

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Declaration of Conflict of Interest

The authors declare the following competing financial interest(s): A.I.K. is a member of the Board of Directors and a part-owner of Q-Chem, Inc.