Since 2002 Perimeter Institute has been recording seminars, conference talks, and public outreach events using video cameras installed in our lecture theatres. Perimeter now has 7 formal presentation spaces for its many scientific conferences, seminars, workshops and educational outreach activities, all with advanced audio-visual technical capabilities. Recordings of events in these areas are all available On-Demand from this Video Library and on Perimeter Institute Recorded Seminar Archive (PIRSA). PIRSA is a permanent, free, searchable, and citable archive of recorded seminars from relevant bodies in physics. This resource has been partially modelled after Cornell University's arXiv.org.
Motivated by the cluster structure of two-loop scattering amplitudes in N = 4 Yang-Mills theory we define cluster polylogarithm functions. We find that all such functions of weight 4 are made up of a single simple building block associated to the A2 cluster algebra. Adding the requirement of locality on generalized Stasheff polytopes, we find that these A2 building blocks arrange themselves to form a unique function associated to the A3 cluster algebra.
Statistical mechanics is the framework that connects thermodynamics to the microscopic world. It hinges on the assumption of equilibration; when equilibration fails, so does much of our understanding. In isolated quantum systems, this breakdown is captured by the phenomenon known as many-body localization. This breakdown manifests in a variety of ways, as elucidated by much recent theoretical and numerical work.
In a conventional Mott insulator, magnitude of local spin moments remain fixed. They are `fixed spin Mott insulators'. We suggest that, in a multi orbital Hubbard model, when local Hund coupling is won over by inter-orbital superexchange couplings between neighboring sites, local spin moment can decrease its value in a cooperative fashion, through a first order phase transition, These are `Low spin state Mott insulators' (LSSMI).
While there is mounting numerical evidence for a gapped Z2 spin liquid in the kagome Heisenberg model, a complete characterization of this topological phase remains to be accomplished. A defining property, the projective symmetry group (PSG) which fixes how the emergent excitations of the spin liquid phase transform under symmetry, remains to be determined. Following a Chern-Simons field theory, we show how PSG determines measurable properties of a Z2 spin liquid, such as the existence of symmetry protected gapless edge states.