The fractional quantum Hall effect, being one of the most studied phenomena in condensed
matter physics during the past 30 years, has generated many ground-breaking new ideas …

We review the progress in the last 20–30 years, during which we discovered that there are
many new phases of matter that are beyond the traditional Landau symmetry breaking …

Topological Phases of Matter are an exceptionally dynamic field of research: several of the
most exciting recent experimental discoveries and conceptual advances in modern physics …

This review presents an entry-level introduction to topological quantum computation--
quantum computing with anyons. We introduce anyons at the system-independent level of …

Is there a vector space whose dimension is the golden ratio? Of course not--the golden ratio
is not an integer! But this can happen for generalizations of vector spaces--objects of a …

A large class of gapped phases of matter can be described by topological finite group gauge
theories. In this paper, we show how such gauge theories possess a higher-group global …

It has recently been realized that a general class of non-Abelian defects can be created in
conventional topological states by introducing extrinsic defects, such as lattice dislocations …

Instead of studying anyon condensation in various concrete models, we take a bootstrap
approach by considering an abstract situation, in which an anyon condensation happens in …

We classify discrete-rotation symmetric topological crystalline superconductors (TCS) in two
dimensions and provide the criteria for a zero-energy Majorana bound state (MBS) to be …

Levin-Wen models are microscopic spin models for topological phases of matter in (2+ 1)-
dimension. We introduce a generalization of such models to (3+ 1)-dimension based on …