1. Chiral Floquet Phases of Many-Body Localized Boson Po Fidkowski, Morimoto, Potter, and Vishwanath. Phys. Rev. X 6, 041070 (2016). Chiral topological phases feature unidirectional transport of quantities such as energy or charge around the edge. Can chiral phases exist in settings where neither charge nor energy is conserved? We find that, nonetheless, chiral phases are tenable in such systems. Instead of charge or energy, quantum information is pumped around the edges. |

### 2. Radical chiral Floquet phases in a periodically driven Kitaev model and beyond.

Po Fidkowski, Morimoto, Potter, and Vishwanath. Phys. Rev. X 6, 041070 (2016). Chiral topological phases feature unidirectional transport of quantities such as energy or charge around the edge. Can chiral phases exist in settings where neither charge nor energy is conserved? We find that, nonetheless, chiral phases are tenable in such systems. Instead of charge or energy, quantum information is pumped around the edges. |

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3. Many Body Localization and topological phases

(with Yasaman Bahri, Vosk, Altman), 2013. arXiv:1307.4092

Here, we extended the concept of a topological state of matter, usually sharply defined only in the quantum ground state, to highly excited states of a correlated quantum system, which is in a many-body localized phase. Specifically we considered a 1 dimensional system which realizes a symmetry protected topological phase. We demonstrate that in this case the bulk topology can give rise to a protected q-bit at the edge, surprisingly, even when the system is very 'hot' and strongly coupled to the degrees of freedom making up the q-bit.

Our work goes beyond parallel works establishing the existence of such phases, by demonstrating a quantum coherent spin-echo response, without the need to cool into the ground state of the system. Normally, achieving quantum coherence requires cooling to extremely low temperatures, which is a major obstruction toward practical realizations. The conceptual advance we make is to show that a class of systems exist where no cooling is needed to attain quantum coherent responses. This result is enabled by a combination of topology and strong disorder, which preserve the topological structure, not only in the ground states, but in all of the exponentially many states of the spectrum.

Here, the topological phase paradoxically appears to gain stability from disorder.