# Theory Seminar: Symmetries, topological order and open systems

Caroline de Groot (MPQ)
In part 1, I'll describe work done with Alex Turzillo and Norbert Schuch in which we address the question of whether symmetry protected topological order (SPTO) exists in open systems by preserving both equivalence classes and order parameters.

November 10, 2021

Caroline de Groot (MPQ)
Group seminar (hybrid format: online/seminar room B0.32)
Wed 10. November 2021, 11:30 am (MEZ)

Abstract:

In part 1, I'll describe work done with Alex Turzillo and Norbert Schuch in which we address the question of whether symmetry protected topological order (SPTO) exists in open systems by preserving both equivalence classes and order parameters. To this end we consider which symmetric channels map within a manifold of SPT mixed states, which we define. Firstly, our main result is proving that a strong symmetry (SS) condition on channels maps a one-dimensional SPT phase $\omega$ to itself and equivalently maps a string order parameter's pattern of zeros back to the same pattern of zeros at finite time which allows us to define an equivalence class of SPT mixed states through fast dissipative Lindbladian evolution (Coser and Perez-Garcia, 2019). We crucially show that a notion of weak symmetry (WS) is too coarse-grained to preserve SPTO. We explore physical observables such as string order and inaccessible entanglement; notably single-site WS destroys the string order parameter instantly with any finite decay, while SS preserves it at longer times. Our second result comes from requiring necessity of preservation of the pattern of zeros which leads us to introduce twisted SS conditions $\sigma$-SS which induce endomorphisms $\sigma$ on the SPT phase and map SPT mixed states to SPT mixed states in a different phase, leading to a new lower bound on inaccessible entanglement. In part 2, if there's time, we will discuss how these results may apply to symmetry enriched topological order (SETO) by applying noise to a particular 2D model with SETO, namely a toric code enriched by cluster states on all loops, which is an ongoing work with Jose Garre Rubio and Alex Turzillo.

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