We examine the interplay of symmetry and topological order in 2+ 1-dimensional topological
quantum phases of matter. We present a precise definition of the topological symmetry …

We investigate mixed states exhibiting nontrivial topological features, focusing on symmetry-
protected topological (SPT) phases under various types of decoherence. Our findings …

We reconsider the problem of electrically charged, massless fermions scattering off
magnetic monopoles. The interpretation of the outgoing states has long been a puzzle as, in …

In this work, we introduce a new type of topological order that is protected by subsystem
symmetries that act on lower-dimensional subsets of lattice many-body system, eg, along …

In a periodically driven (Floquet) system, there is the possibility for new phases of matter, not
present in stationary systems, protected by discrete time-translation symmetry. This includes …

We put the theory of interacting topological crystalline phases on a systematic footing. These
are topological phases protected by space-group symmetries. Our central tool is an …

A system with charge conservation and lattice translation symmetry has a well-defined filling
ν, which is a real number representing the average charge per unit cell. We show that if ν is …

A bstract We discuss bosonization and Fermionic Short-Range-Entangled (FSRE) phases of
matter in one, two, and three spatial dimensions, emphasizing the physical meaning of the …

Average symmetry-protected topological (ASPT) phase is a generalization of symmetry-
protected topological phases to disordered systems or open quantum systems. We devise a" …

We provide a classification of invertible topological phases of interacting fermions with
symmetry in two spatial dimensions for general fermionic symmetry groups G f and general …