Semidefinite relaxation of multi-marginal optimal transport for strictly correlated electrons in second quantization

Understand

We consider the strictly correlated electron (SCE) limit of the fermionic quantum many-body problem in the second-quantized formalism.

• This limit gives rise to a multi-marginal optimal transport (MMOT) problem.
• Here the marginal state space for our MMOT problem is the binary set $\{0,1\}$, and the number of marginals is the number $L$ of sites in the model.
• The costs of storing and computing the exact solution of the MMOT problem both scale exponentially with respect to $L$.