Gapless Topological Phases and Symmetry-Enriched Quantum Criticality

Equivariant Topological Quantum Field Theory and Symmetry Protected Topological Phases

Short-range entangled topological phases of matter are closely connected to Topological Quantum Field Theory. We use this connection to classify Symmetry Protected Topological Phases in low dimensions, including the case when the symmetry involves time-reversal. To accomplish this, we generalize Turaev’s description of equivariant TQFT to the unoriented case. We show that invertible unoriented ...

Symmetry Protected Topological phases of Quantum Matter

We describe recent progress in our understanding of the interplay between interactions, symmetry, and topology in states of quantum matter. We focus on a minimal generalization of the celebrated topological band insulators to interacting many particle systems, known as Symmetry Protected Topological (SPT) phases. In common with the topological band insulators these states have a bulk gap and no...

Translational Symmetry and Microscopic Constraints on Symmetry-Enriched Topological Phases: A View from the Surface

The Lieb-Schultz-Mattis theorem and its higher-dimensional generalizations by Oshikawa and Hastings require that translationally invariant 2D spin systems with a half-integer spin per unit cell must either have a continuum of low energy excitations, spontaneously break some symmetries, or exhibit topological order with anyonic excitations. We establish a connection between these constraints and...

Numerical detection of symmetry enriched topological phases with space group symmetry

Topologically ordered phases of matter, in particular so-called symmetry enriched topological (SET) phases, can exhibit quantum number fractionalization in the presence of global symmetry. In Z2 topologically ordered states in two dimensions, fundamental translations Tx and Ty acting on anyons can either commute or anticommute. This property, crystal momentum fractionalization, can be seen in a...

Topological phases and quantum computation