Designing superconducting quantum circuits that exhibit gapless symmetry protected topological phases

Symmetry protected topological (SPT) phases give rise to exponentially localized edge modes and are characterized by the presence of a gap in the spectrum. A well-known example is the spin-1 Haldane chain/AKLT model, which hosts protected spin-1/2 degrees of freedom at the boundaries. Unlike suchstandard SPT phases, there exist systems that exhibit protected edge modes even in the presence of gapless degrees of freedom and hence are called gapless symmetry protected topological (GSPT) phases. In this talk, we propose superconducting quantum circuits whose low-energy degrees of freedom realize GSPT phases. Our circuits provide a route to exhibiting novel topological phases of matter; in addition, their emergent Majorana zero modes could possibly serve as topologically-protected qubits.