Papers › Exact solution of the many-body problem with a 𝒪(n⁶) complexity
Exact solution of the many-body problem with a 𝒪(n⁶) complexity
Thierry Deutsch
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In this article, we define a new mathematical object, called a pair D=(A,C) of anti-commutation matrices (ACMP) based on the anti-commutation relation a^†ᵢaⱼ + aⱼa^†ᵢ = δᵢⱼ applied to the scalar product between the many-body wavefunctions. This ACMP explicitly separates the different levels of correlation. The one-body correlations are defined by a ACMP D⁰=(A⁰,C⁰) and the two-body ones by a set of n ACMPs Dⁱ=(Aⁱ,Cⁱ) where n is the number of states. We show that we can have a compact and exact parametrization with n⁴ parameters of the two-body reduced density matrix (\TRDM) of any pure or mixed N-body state to determine the ground state energy with a 𝒪(n⁶) complexity.
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