Topological Phases of Matter: June 10-14, 2013

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
slides
10:30am Coffee Break Simons Center Cafe
11:00am Braiding Defects in Symmetry Enriched Topological Phases Netanel Lindner video
slides
12:00pm Lunch Simons Center Cafe
 1:15pm Emergent Space-time Supersymmetry in Topological Superconductors Tarun Grover video
slides
 2:30pm Symmetry protected topological phases and orbifolds Shinsei Ryu video
slides
 3:30pm Tea Time SCGP 515
 4:15pm Protected edge modes without symmetry Michael Levin video
slides


Time Title Presenters  Video
 9:30am Novel Topological Phases and Surface States in Interacting Systems Ashvin Vishwanath video
slides
10:30am Coffee Break Simons Center Cafe
11:00am Universal topological quantum computation from a fractionalized superconductor Jason Alicea video
slides
12:00pm Lunch Simons Center Cafe
 1:15pm Entanglement of quantum Hall states, and conformal field theory Jerome Dubail video
slides
 2:30pm Gravitational responses from entanglement Michael Zaletel video
slides
 3:30pm Tea Time SCGP 515
 4:00pm Topological invariants for fractional quantum Hall states Victor Gurarie video
slides
 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
slides
10:30am Coffee Break Simons Center Cafe
11:00am Twisted Equivariant Matter Gregory Moore video
slides
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
slides
 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
slides
12:00pm Lunch Simons Center Cafe
 1:15pm A Z_n generlization of honeycomb Kitaev model Xiao-Liang Qi video
slides
 2:30pm Bulk entanglement spectrum reveals quantum criticality
within a topological state
Liang Fu video
slides
 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
slides
10:30am Coffee Break Simons Center Cafe
11:00am Characterizing topological order by studying the ground states of an infinite cylinder Lukasz Cincio video
slides
12:00pm Lunch Simons Center Cafe
 3:30pm Tea Time SCGP 515