Higher-Order Symmetry Enriched Topological Phases

Higher-order topological insulators (TIs) exhibit boundary physics typically associated with lower dimensional TIs, e.g. 2-d second-order TIs exhibit localized 0-d zero energy corner modes. This physics is topologically protected as long as certain lattice symmetries are preserved, akin to topological crystalline insulators. So far, these phases have largely been explored in the context of non-interacting fermion systems. However, we know that symmetries may also "enrich" the physics of interacting topological phases, such as quantum spin liquids or fractional quantum Hall states. Is it possible to realize "higher-order" boundary physics in strongly interacting topological phases? In this talk, we discuss exactly such higher-order symmetry enriched topological phases, including an example of an exactly solvable spin model with a quantum spin liquid ground state that indeed exhibits topologically protected corner modes, a hallmark of second-order TIs.