A path integral study of the role of correlation in exchange coupling of spins in double quantum dots and optical lattices

We explore exchange coupling of a pair of spins in a double dot and in an optical lattice, using the frequency of exchanges in a bosonic path integral, evaluated using MonteCarlo simulation. The algorithm gives insights into the role of correlation through visualization of two-particle probability densities, instantons, and the correlation hole. We map the problem to the Hubbard model and see that exchange and correlation renormalize the model parameters, dramatically reducing the effective on-site repulsion at larger separations.