Organized by Paul Fendley (University of Virginia), Andreas Ludwig (UCSB), Xiao-Liang Qi (Stanford), Nicholas Read (Yale), Steven Simon (Oxford) and Zhenghan Wang (Microsoft Station Q)

Attendee List Download Talk Schedule Download PosterView Videos

A topological phase of matter can be broadly defined as a (quantum-mechanical) phase of matter in which the ground state has a gap for all local excitations. This seemingly uninspiring definition gives rise to interesting phenomena for a number of reasons. Ground state correlation functions of local operators decay exponentially fast with distance, so the leading asymptotically low-energy (below the scale of the gap) and long-distance observable properties will be independent of the metric or of the length scale in the correlation functions|they are topological invariants (however, such observables might all be zero, giving the trivial topological phase). Moreover, the observable properties will remain unchanged under a small change in Hamiltonian, because the Hamiltonian is the integral over space of a local operator, which cannot affect the topological observables. Examples of such topological observable properties are (i) the Hall conductivity, which is quantized (but possibly zero) in these systems; (ii) ground state degeneracy when the space on which the phase lives is topologically non-trivial, for example a 2-torus as opposed to a 2-sphere; (iii) existence of \topologically non-trivial” quasiparticle excitations above the true ground state, and the quantum numbers and non-trivial statistics (behavior under adiabatic braiding) of these are topological properties (the braiding is equivalent to expectation values of knots or links formed by Wilson lines in spacetime). Related topologically \protected” effects include (iv) gapless excitations on the boundary of a region filled by the topological phase, which may be described by a conformal field theory, and cannot be rendered gapped (massive) by any perturbation in the Hamiltonian. Most importantly, topological phases exist in nature, and more are being discovered. Many are two-dimensional, but examples in three dimensions are now being uncovered. Theory is leading experiment: for example, three-dimensional topological insulators were predicted, then confirmed.

This workshop is part of the Spring 2013 program Topological phases of matter, Organized by Nick Read

#### Topological Phases of Matter Workshop Schedule

Time | Title | Presenters | Video |

9:30am | SPT phases, gauge anomalies, and lattice definition of all anomaly-free chiral gauge theories | Xiao-Gang Wen | video |

10:30am | Coffee Break | Simons Center Cafe | |

11:00am | Braiding Defects in Symmetry Enriched Topological Phases | Netanel Lindner | video |

12:00pm | Lunch | Simons Center Cafe | |

1:15pm | Emergent Space-time Supersymmetry in Topological Superconductors | Tarun Grover | video |

2:30pm | Symmetry protected topological phases and orbifolds | Shinsei Ryu | video |

3:30pm | Tea Time | SCGP 515 | |

4:15pm | Protected edge modes without symmetry | Michael Levin | video |

Time | Title | Presenters | Video |

9:30am | Novel Topological Phases and Surface States in Interacting Systems | Ashvin Vishwanath | video |

10:30am | Coffee Break | Simons Center Cafe | |

11:00am | Universal topological quantum computation from a fractionalized superconductor | Jason Alicea | video |

12:00pm | Lunch | Simons Center Cafe | |

1:15pm | Entanglement of quantum Hall states, and conformal field theory | Jerome Dubail | video |

2:30pm | Gravitational responses from entanglement | Michael Zaletel | video |

3:30pm | Tea Time | SCGP 515 | |

4:00pm | Topological invariants for fractional quantum Hall states | Victor Gurarie | video |

5:00pm | PATHS Exhibition Closing Reception: Wine and Cheese Reception | Simons Center Lobby | |

5:30pm | PATHS Exhibition Closing Reception: Lecture featuring W. Brad Paley | Simons Center Auditorium |

Time | Title | Presenters | Video |

9:30am | Topological Delocalization, Average Symmetry and Symplectic Anderson Transition | Charlie Kane | video |

10:30am | Coffee Break | Simons Center Cafe | |

11:00am | Twisted Equivariant Matter | Gregory Moore | video |

12:00pm | Lunch | Simons Center Cafe | |

1:15pm | Stability of Area Laws and Emergence of Quasi-Particles in Quantum Many Body Systems | Frank Verstraete | video |

2:30pm | Truncated Conformal Field Theory and Fractional Quantum Hall Matrix Product States | Andrei Bernevig | video |

3:30pm | Tea Time | SCGP 515 |

Time | Title | Presenters | Video |

9:30am | Free parafermions | Paul Fendley | video |

10:30am | Coffee Break | Simons Center Cafe | |

11:00am | Entanglement sum rules | Brian Swingle | video |

12:00pm | Lunch | Simons Center Cafe | |

1:15pm | A Z_n generlization of honeycomb Kitaev model | Xiao-Liang Qi | video |

2:30pm | Bulk entanglement spectrum reveals quantum criticality within a topological state |
Liang Fu | video |

3:30pm | Tea Time | SCGP 515 | |

6:00pm | Workshop Banquet | Simons Center Cafe |

Time | Title | Presenters | Video |

9:30am | Condensation and critical spin chains | Eddy Ardonne | video |

10:30am | Coffee Break | Simons Center Cafe | |

11:00am | Characterizing topological order by studying the ground states of an infinite cylinder | Lukasz Cincio | video |

12:00pm | Lunch | Simons Center Cafe | |

3:30pm | Tea Time | SCGP 515 |