Parafermions and symmetry-enriched Majorana fermions in one-dimensional fermionic models
Christophe Mora (Laboratoire Pierre Aigrain, ENS, Paris)
Stabilizing and manipulating exotic emergent quasiparticles is one of the main goal of modern condensed matter physics. The quest for observing Majorana fermions and their non-Abelian braiding statistics in superconducting nanostructures is currently attracting a lot of attention, with fascinating prospects in fault-tolerant quantum computation. Parafermions are the simplest generalization of Majorana fermions: they show non-Abelian fractional statistics and are typically associated with topological phases. We will discuss the possibility of harboring these exotic excitations in genuinely one-dimensional electronic platforms. We focus on a specific model of fermions in one dimension with a generalized ZN multiplet pairing extending the standard and so-called Kitaev chain model. Using a combination of analytical techniques, we find an interesting topological phase intertwined with spontaneous symmetry breaking. Each symmetry-breaking sector is shown to possess a pair of boundary Majorana fermions encoding a topological character. A careful study of the quantum anomaly through pumping in the system finally reveals that parafermions exist in one dimension but only as non-local operators.
- Fernando Iemini, Christophe Mora & Leonardo Mazza, Topological phases of parafermions: a model with exactly-solvable ground states, Phys. Rev. Lett. 118, 170402 (2017)
- Leonardo Mazza, Fernando Iemini, Marcello Dalmonte & Christophe Mora, Poor man’s parafermions in a lattice model with even multiplet pairing, preprint cond-mat arXiv:1801.08548.