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.
We study a superconductor-ferromagnet-superconductor (SC-FM-SC) Josephson junction array deposited on top of a two-dimensional quantum spin Hall (QSH) insulator. The existence of Majorana bound states at the interface between SC and FM gives rise to charge-e tunneling, in addition to the usual charge-2e Cooper pair tunneling, between neighboring superconductor islands.
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I will discuss the question of thermal stability of a passive quantum memory, or finite-temperature topological order, in two or three spatial dimensions. We will analyze the criteria for thermal stability. We will present new results on Majorana fermion codes and a new extension of the 2D surface code to three dimensions.
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Anyons are a special kind of excitations which are allowed in two dimensional systems, along with fermions and bosons. The topological nature of braiding of non-abelian anyons may allow a realization of quantum computing gates which is immune to noise. While the insensitivity of the such systems to a localized noise source is a built-in feature, an issue of great importance is more subtle: the robustness to slight deformations of the amiltonian describing the phase by perturbations which are locally tiny but are spread over through the entire system.
Adiabatic evolutions connect two gapped quantum states in the same phase. We argue that the adiabatic evolutions are closely related to local unitary transformations which define a equivalence relation. So the equivalence classes of the local unitary transformations are the universality classes that define the different phases of quantum system. Since local unitary transformations can remove local entanglements, the above equivalence/universality classes correspond to pattern of long range entanglement, which is the essence of topological order.
Many crystalline materials predicted by band theory to be metals are insulators due to strong electron interactions. Both experiment and theory suggest that such Mott-insulators can exhibit exotic gapless spin-liquid ground states, having no magnetic or any other order. Such “critical spin liquids” will possess power law spin correlations which oscillate at various wavevectors. In a sub-class dubbed “Spin Bose-Metals” the singularities reside along surfaces in momentum space, analogous to a Fermi surface but without long-lived quasiparticle excitations.
I discuss a class of systems with a very special property: exact results for physical quantities can be found in the many-body limit in terms of the original (bare) parameters in the Hamiltonian. A classic result of this type is Onsager and Yang's formula for the magnetization in the Ising model. I show how analogous results occur in a fermion chain with strong interactions, closely related to the XXZ spin chain. This is done by exploiting a supersymmetry, and noting that certain quantites are independent of finite-size effects.
In the Ho2Ti2O7 and Dy2Ti2O7 magnetic pyrochlore oxides, the Ho and Dy Ising magnetic moments interact via geometrically frustrated effective ferromagnetic coupling. These systems possess and extensive zero entropy related to the extensive entropy of ice water -- hence the name spin ice. The classical ground states of spin ice obey a constraint on each individual tetrahedron of interacting spins -- the so-called "ice rules". At large distance, the ice-rules can be described by an effective divergent-free field and, therefore, by an emergent classical gauge theory.
Many one dimensional random quantum systems exhibit infinite randomness phases, such as the random singlet phase of the spin-1/2 Heisenberg model. These phases are typically the result of destabilizing systems described by a conformal field theory with disorder. Interestingly, entanglement entropy in 1d infinite randomness phases also exhibits a universal log scaling with length.