A Baker-Campbell-Hausdorff formula for the logarithm of permutations
Quantum Physics
2020-04-23 v1 Mathematical Physics
math.MP
Abstract
The dynamics-from-permutations of classical Ising spins is studied for a chain of four spins. We obtain the Hamiltonian operator which is equivalent to the unitary permutation matrix that encodes assumed pairwise exchange interactions. It is shown how this can be summarized by an exact terminating Baker-Campbell-Hausdorff formula, which relates the Hamiltonian to a product of exponentiated two-spin exchange permutations. We briefly comment upon physical motivation and implications of this study.
Keywords
Cite
@article{arxiv.2001.11909,
title = {A Baker-Campbell-Hausdorff formula for the logarithm of permutations},
author = {Hans-Thomas Elze},
journal= {arXiv preprint arXiv:2001.11909},
year = {2020}
}
Comments
11 pages; see also arXiv:2001.10907, especially for more references; accepted and to appear in Int. J. Geom. Meth. Mod. Phys. (IJGMMP)