Topological matter

Topological phases, such as fractional quantum Hall states, are phases with no local order parameter and are instead characterized by more exotic quantities such as peculiar entanglement properties. The interest in topological phases stems to a large degree from the exotic nature of excitations in such systems, which not only carry fractional charge but also obey unusual statistics: when two such excitations, called anyons, are exchanged, they - in contrast to fermions that pick up a phase of π - can pick up a phase that can be a fraction of π. What is even more exotic is that certain topological phases have excitations that map the manybody wavefunction from one orthogonal state to another under exchange - such non-abelian anyons can be used to realize the dream of fault-tolerant topological quantum computation, which is intrinsically robust to errors. We are interested in understanding the structure, including entanglement structure, of topological matter, as well as finding ways to prepare topological states and study them in and out of equilibrium.