How to define quantum mean-field solvable Hamiltonians using Lie algebras

• URL: http://arxiv.org/abs/2008.06633v3
• Date: Fri, 11 Jun 2021 02:17:56 GMT
• Title: How to define quantum mean-field solvable Hamiltonians using Lie algebras
• Authors: Artur F. Izmaylov and Tzu-Ching Yen
• Abstract summary: We define what mean-field theory is, independently of a Hamiltonian realization in a particular set of operators. We then formulate a criterion for a Hamiltonian to be mean-field solvable. For the electronic Hamiltonians, our approach reveals the existence of mean-field solvable Hamiltonians of higher fermionic operator powers than quadratic.
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Necessary and sufficient conditions for quantum Hamiltonians to be exactly solvable within mean-field theories have not been formulated so far. To resolve this problem, first, we define what mean-field theory is, independently of a Hamiltonian realization in a particular set of operators. Second, using a Lie-algebraic framework we formulate a criterion for a Hamiltonian to be mean-field solvable. The criterion is applicable for both distinguishable and indistinguishable particle cases. For the electronic Hamiltonians, our approach reveals the existence of mean-field solvable Hamiltonians of higher fermionic operator powers than quadratic. Some of the mean-field solvable Hamiltonians require different sets of quasi-particle rotations for different eigenstates, which reflects a more complicated structure of such Hamiltonians.

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