Exact solution of the many-body problem with a $\mathcal{O}\left(n^6\right)$ complexity
Exact solution of the many-body problem with a $\mathcal{O}\left(n^6\right)$ complexity
In this article, we define a new mathematical object, called a pair of anti-commutant density matrices (ACDM) based on the relation $a^\dag_{i} a_{j} + a_{j} a^\dag_{i} = \delta_{ij}$ applied to the scalar product between the many-body wavefunctions. These new objects form a Hilbert space $\mathcal{D}_N$ isomorph to the usual Hilbert …