Maissam Barkeshli

Correlated topological insulators and the fractional magnetoelectric effect

Topological insulators are characterized by the presence of gapless surface modes protected by time-reversal symmetry. In three space dimensions the magnetoelectric response is described in terms of a bulk

Classification of Topological Defects in Abelian Topological States

\ensuremath{\theta}

Continuous transition between fractional quantum Hall and superfluid states

term for the electromagnetic field. Here we construct theoretical examples of such phases that cannot be smoothly connected to any band insulator. Such correlated topological insulators admit the possibility of fractional magnetoelectric response described by fractional

Particle-hole symmetry and the composite Fermi liquid

\ensuremath{\theta}/\ensuremath{\pi}

Anyon Condensation and Continuous Topological Phase Transitions in Non-Abelian Fractional Quantum Hall States

. We show that fractional

Structure of quasiparticles and their fusion algebra in fractional quantum Hall states

\ensuremath{\theta}/\ensuremath{\pi}

U(1)×U(1)⋊Z2Chern-Simons theory andZ4parafermion fractional quantum Hall states

is only possible in a gapped time-reversal-invariant system of bosons or fermions if the system also has deconfined fractional excitations and associated degenerate ground states on topologically nontrivial spaces. We illustrate this result with a concrete example of a time-reversal-symmetric topological insulator of correlated bosons with

Generalized Kitaev models and extrinsic non-Abelian twist defects.

\ensuremath{\theta}=\frac{\ensuremath{\pi}}{4}

Continuous transitions between composite Fermi liquid and Landau Fermi liquid: A route to fractionalized Mott insulators

. Extensions to electronic fractional topological insulators are briefly described.

Effective field theory and projective construction for Z{sub k} parafermion fractional quantum Hall states

In this paper we propose the most general classification of point-like and line-like extrinsic topological defects in (2+1)-dimensional Abelian topological states. We first map generic extrinsic defects to boundary defects, and then provide a classification of the latter. Based on this classification, the most generic point defects can be understood as domain walls between topologically distinct boundary regions. We show that topologically distinct boundaries can themselves be classified by certain maximal subgroups of mutually bosonic quasiparticles, called Lagrangian subgroups. We study the topological properties of the point defects, including their quantum dimension, localized zero modes, and projective braiding statistics.