Semidefinite Relaxation of Multimarginal Optimal Transport for Strictly Correlated Electrons in Second Quantization

Adiabatic connection for strictly correlated electrons.

Modern density functional theory (DFT) calculations employ the Kohn-Sham system of noninteracting electrons as a reference, with all complications buried in the exchange-correlation energy (E(XC)). The adiabatic connection formula gives an exact expression for E(XC). We consider DFT calculations that instead employ a reference of strictly correlated electrons. We define a "decorrelation energy"...

Semidefinite relaxation for dominating set

‎It is a well-known fact that finding a minimum dominating set and consequently the domination number of a general graph is an NP-complete problem‎. ‎In this paper‎, ‎we first model it as a nonlinear binary optimization problem and then extract two closely related semidefinite relaxations‎. ‎For each of these relaxations‎, ‎different rounding algorithm is exp...

A semidefinite relaxation scheme for quadratically constrained

  Semidefinite optimization relaxations are among the widely used approaches to find global optimal or approximate solutions for many nonconvex problems. Here, we consider a specific quadratically constrained quadratic problem with an additional linear constraint. We prove that under certain conditions the semidefinite relaxation approach enables us to find a global optimal solution of the unde...

The adiabatic strictly-correlated-electrons functional: kernel and exact properties.

We investigate a number of formal properties of the adiabatic strictly-correlated electrons (SCE) functional, relevant for time-dependent potentials and for kernels in linear response time-dependent density functional theory. Among the former, we focus on the compliance to constraints of exact many-body theories, such as the generalised translational invariance and the zero-force theorem. Withi...

Transport of One-Dimensional Correlated Electrons