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#### Abstract

This tool illustrates the calculation of spin coupling in neighboring quantum dots. The theory behind this calculation is described in “Path integral study of the role of correlation in exchange coupling
in quantum dots and optical lattices,” by Lei Zhang, M. J. Gilbert, and J. Shumway (submitted, 2008). The model is a double parabolic quantum dot, and the user may adjust several parameters, including:

- The dot separation distance.
- The electron effective mass.
- The dielectric constant.

- The interacting charge density in cm
^{-2}. - The spin coupling J in meV.
- The correlation hole when one electron is passing between the dots.

*Note:*To get precise answers, the simulations must be converged with respect to time step (Trotter number) and sampled thoroughly. Also, the temperature must be low enough to suppress contributions from double occupation of dots. The results and errorbars nanoHUB are a rough guide to the value of the exchange splittings and serve to illustrate this path integral method. You may contact john.shumway@asu.edu for expert advise if you intend to use these results in research applications.#### Powered by

“pi”: our group’s open-source path integral Monte Carlo program.

The full path integral simulation tool available as app-pimc on nanoHUB.

#### Credits

Developed by John Shumway in the Department of Physics at Arizona State University.

#### Sponsored by

Work supported by NSF Grant No. DMR 0239819 and NRI-SWAN.

#### References

- “Path integral study of the role of correlation in exchange coupling in quantum dots and optical lattices,” by Lei Zhang, M. J. Gilbert, and J. Shumway (submitted, 2008).
- Double dot model is from: J. Pedersen, C. Flindt, N. A. Mortensen, and A.-P. Jauho, Phys. Rev. B 76, 125323 (2007).

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