Andrew M. Essin

Bulk-boundary correspondence of topological insulators from their respective Green’s functions

Topological insulators are noninteracting, gapped fermionic systems which have gapless boundary excitations. They are characterized by topological invariants, which can be written in many different ways, including in terms of Greens functions. Here we show that the existence of the edge states directly follows from the existence of the topological invariant written in terms of the Greens functions, for all ten classes of topological insulators in all spatial dimensions. We also show that the resulting edge states are characterized by their own topological invariant, whose value is equal to the topological invariant of the bulk insulator. This can be used to test whether a given model Hamiltonian can describe an edge of a topological insulator. Finally, we observe that the results discussed here apply equally well to interacting topological insulators, with certain modifications.

Classifying fractionalization: symmetry classification of gapped Z2 spin liquids in two dimensions

We classify distinct types of quantum number fractionalization occurring in two-dimensional topologically ordered phases, focusing in particular on phases with

Topological insulators beyond the Brillouin zone via Chern parity

{\mathbb{Z}}_{2}

Approximating the Sachdev-Ye-Kitaev model with Majorana wires

topological order, that is, on gapped

Topological invariants and interacting one-dimensional fermionic systems

{\mathbb{Z}}_{2}

Z2topological invariants in two dimensions from quantum Monte Carlo

spin liquids. We find that the fractionalization class of each anyon is an equivalence class of projective representations of the symmetry group, corresponding to elements of the cohomology group

Majorana spin liquids and projective realization of SU(2) spin symmetry

{H}^{2}(G,{\mathbb{Z}}_{2})

Antiferromagnetic topological insulators in cold atomic gases

. This result leads us to a symmetry classification of gapped

Anomalous Quasiparticle Symmetries and Non-Abelian Defects on Symmetrically Gapped Surfaces of Weak Topological Insulators.

{\mathbb{Z}}_{2}

Topological invariants for fractional quantum Hall states

spin liquids, such that two phases in different symmetry classes cannot be connected without breaking symmetry or crossing a phase transition. Symmetry classes are defined by specifying a fractionalization class for each type of anyon. The fusion rules of anyons play a crucial role in determining the symmetry classes. For translation and internal symmetries, braiding statistics plays no role, but can affect the classification when point group symmetries are present. For square lattice space group, time-reversal, and