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

TL;DR

This paper presents a Monte Carlo-based path integral method to analyze how electron correlation affects exchange coupling in double quantum dots and optical lattices, providing new insights into the underlying physics.

Contribution

It introduces a simple, black-box Monte Carlo algorithm for studying exchange coupling and correlation effects, mapping the problem to the Hubbard model for better understanding.

Findings

Correlation significantly lowers the effective U at larger separations.

The algorithm offers visualizations of instantons and pair correlation functions.

Exchange and correlation effects renormalize Hubbard model parameters.

Abstract

We explore exchange coupling of a pair of spins in a double dot and in an optical lattice. Our algorithm uses the frequency of exchanges in a bosonic path integral, evaluated with Monte Carlo. This algorithm is simple enough to be a "black box" calculator, yet gives insights into the role of correlation through two-particle probability densities, visualization of instantons, and pair correlation functions. We map the problem to Hubbard model and see that exchange and correlation renormalize the effective parameters, dramatically lowering U at larger separations.