A curious mapping between supersymmetric quantum chains

TL;DR

This paper introduces a unitary transformation linking two distinct supersymmetric quantum chain models, revealing a deep connection and generalizing known sign factors in fermionic transformations.

Contribution

It presents a novel unitary mapping between two different supersymmetric lattice models, expanding understanding of their underlying symmetries and relationships.

Findings

Established a unitary transformation between two supersymmetric models

Generalized sign factors in fermionic transformations

Revealed a deep connection between seemingly different models

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.