Exact solution of the many-body problem with a
$\mathcal{O}\left(n^6\right)$ complexity
- URL: http://arxiv.org/abs/2111.15281v3
- Date: Thu, 9 Jun 2022 13:06:12 GMT
- Title: Exact solution of the many-body problem with a
$\mathcal{O}\left(n^6\right)$ complexity
- Authors: Thierry Deutsch
- Abstract summary: We define a new mathematical object, called a pair $=left(ACright)$ of anti-commutation matrices (ACMP)
We show that we can have a compact and exact parametrization with a $mathcalOleft(n6right)$ complexity.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: In this article, we define a new mathematical object, called a pair
$D=\left(A,C\right)$ of anti-commutation matrices (ACMP) based on the
anti-commutation relation $a^\dag_{i}a_{j} + a_{j}a^\dag_{i} = \delta_{ij}$
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 $D^0=\left(A^0,C^0\right)$ and the two-body
ones by a set of $n$ ACMPs $D^i=\left(A^i,C^i\right)$ where $n$ is the number
of states. We show that we can have a compact and exact parametrization with
$n^4$ 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
$\mathcal{O}\left(n^6\right)$ complexity.
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