University of Minnesota

## Talks by Fiona Burnell

## Subsystem-Symmetry protected phases of matter

Fiona Burnell
University of Minnesota

We know that different systems with the same unbroken global symmetry can nevertheless be in distinct phases of matter. These different "symmetry-protected topological" phases are characterized by protected (gapless) surface states. After reviewing this physics in interacting systems with global symmetries, I will describe how a different class of symmetries known as subsystem symmetries, which are neither local nor global, can also lead to protected gapless boundaries. I will discuss how some of these subsystem-symmetry protected phases are related (though not equivalent) to interacting

## Time reversal invariant gapped boundaries of the double semion state

Fiona Burnell
University of Minnesota

## 3D topological lattice models with topologically ordered surface states

Fiona Burnell
University of Minnesota

I will discuss a family of solvable 3D lattice models that have a ``trivial" bulk, in which all excitations are confined, but exhibit topologically ordered surface states. I will discuss perturbations to these models that can drive a phase transition in which some of these excitations become deconfined, driving the system into a phase with bulk topological order.

## Building Fractional Topological Insulators

Fiona Burnell
University of Minnesota

Time-reversal invariant band insulators can be separated into two categories: `ordinary' insulators and `topological' insulators. Topological band insulators have low-energy edge modes that cannot be gapped without violating time-reversal symmetry, while ordinary insulators do not. A natural question is whether more exotic time-reversal invariant insulators (insulators not connected adiabatically to band insulators) can also exhibit time-reversal protected edge modes.