How to define quantum mean-field solvable Hamiltonians using Lie algebras. (30th July 2021)

• Record Type: Journal Article
• Authors: Izmaylov, Artur F; Yen, Tzu-Ching
• Is Part Of: Quantum science and technology. Volume 6:Number 4(2021)
• Publication Date: 2021-07-30
• Subjects: mean-field -- Lie algebras -- quantum computing -- exactly solvable; Quantum theory -- Periodicals; Quantum theory; Periodicals; 530
• DOI: 10.1088/2058-9565/ac1040
• Languages: English
• ISSNs: 2058-9565

Abstract

Abstract: Necessary and sufficient conditions for quantum Hamiltonians to be exactly solvable within mean-field (MF) theories have not been formulated so far. To resolve this problem, first, we define what MF 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 MF solvable. The criterion is applicable for both distinguishable and indistinguishable particle cases. For the electronic Hamiltonians, our approach reveals the existence of MF solvable Hamiltonians of higher fermionic operator powers than quadratic. Some of the MF solvable Hamiltonians require different sets of quasi-particle rotations for different eigenstates, which reflects a more complicated structure of such Hamiltonians.