Applications

In these pages interaction distance $D_\mathcal{F}$ is used to analyse models of spin chains and parafermions. (For an introduction to parafermions, see this paper.) Comparisons to analytical solutions are provided where possible.

The Ising Model: $\displaystyle \hat{H} = -\sum_{j=1}^{L}\left(\pm\sigma_{j}^{x}\sigma_{j+1}^{x}+h_{z}\sigma_{j}^{z}+h_{x}\sigma_{j}^{x}\right)$

Parafermion chains: $\displaystyle \hat{H}_{\mathbb{Z}_{N}} = -\sum_{j}\alpha_{2j}^{\dagger}\alpha_{2j+1} - f\sum_{j}\alpha_{2j-1}^{\dagger}\alpha_{2j} + h.c.$