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



A.F. Izmaylov and T.C. Yen


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.


Recommended SciCasts
Introduction to ScienceCast
SoK: Yield Aggregators in DeFi
Quantum chemistry on quantum annealers
Equatorial magnetoplasma waves
Spin-plasma waves
Cosmic Birefringence in 2022
Liquidations: DeFi on a Knife-edge