Topological and symmetry-enriched random quantum critical points

Topological phases represent a pillar of modern condensed matter physics. While gapped topological systems have been studied extensively, gapless topological materials represent an exciting, largely unexplored area. Here, the authors show that symmetry can enrich random quantum critical points and phases. They uncover a class of gapless topological phases, protected by symmetry and robust to strong randomness. Some of these phases can be realized in nonequilibrium states stabilized by many-body localization. They also appear naturally in periodically driven (Floquet) systems.