Defects and degeneracies in supersymmetry protected phases

¹ Institute for Theoretical Physics, University of Amsterdam - Science Park 904, 1098 XH Amsterdam, The Netherlands
² Rudolf Peierls Centre for Theoretical Physics, University of Oxford - 1 Keble Road, Oxford OX1 3NP, UK

Received: 18 May 2015
Accepted: 23 July 2015

Abstract

We analyse a class of 1D lattice models, known as models, which are characterised by an order-k clustering of spin-less fermions and by lattice supersymmetry. Our main result is the identification of a class of (bulk or edge) defects, that are in one-to-one correspondence with so-called spin fields in a corresponding parafermion CFT. In the gapped regime, injecting such defects leads to ground-state degeneracies that are protected by the supersymmetry. The defects, which are closely analogous to quasi-holes over the fermonic Read-Rezayi quantum Hall states, display characteristic fusion rules, which are of Ising type for k = 2 and of Fibonacci type for k = 3.