A curious mapping between supersymmetric quantum chains
arXiv:1710.02658 · doi:10.1007/978-3-030-04161-8_12
Abstract
We present a unitary transformation relating two apparently different supersymmetric lattice models in one dimension. The first \cite{FS07} describes semionic particles on a 1D ladder, with supersymmetry moving particles between the two legs. The second \cite{GFNR15} is a fermionic model with particle-hole symmetry and with supersymmetry creating or annihilating pairs of domain walls. The mapping we display features non-trivial phase factors that generalise the sign factors occurring in the Jordan-Wigner transformation. We dedicate this work to our friend and colleague Bernard Nienhuis, on the occasion of his 65-th birthday.
Proceedings of the workshop Integrability in Low-dimensional Quantum Systems, Mathematical Research Institute (MATRIX), Creswick, VIC, Australia