Mele, "[Z.sub.2]

topological order and the quantum spin hall effect," Physical Review Letters, vol.

The minor order is a generalization of the

topological order, because subdivision removal is just a special case of edge contraction.

Subjects discussed in this volume include a history of the past sixty years of condensed matter physics; spin ice, fractionalization, and

topological order; superconducting microresonators; quantum computation by local measurement; and Bose gases with non-zero spin.

The lecture notes address such concepts as the interplay between conformal field theory and stochastic Loewner evolution, Coulomb gas techniques, tiling models, dimers, the definition of models of random curves on a background of random triangulations, boundary conditions, quantum inverse scattering, spin chains, the interplay between integrable models and combinatorics, mass transport models of condensation in real space, quantum impurity problems, the physics of spin liquids, the quantum Hall effect, models of rotating Bose-Einstein condensates, and models of

topological order with applications to quantum computing.

Actually, it presents and discusses in classic

topological order the theological contents of the Reformed creeds, ranging from revelation, trinity, creation, sin, covenant, justification, and sanctification, to church, sacraments, ministry, and church and state (part 2; 29-264).

Topics for students and researchers include mathematical formulas of atom trap quantum gates, Poisson algebras and Yang-Baxter equations and

topological order and entanglement.

A final thrust of activity will focus on newly-proposed fracton states of matter not captured by usual theories of

topological order, And will employ both analytical parton techniques and numerical quantum monte carlo simulations.

Other topics include superconductors with

topological order, superconductivity in highly correlated systems, Cooper's electron pairs in low-temperature superconductors, charge carrier localization in plumbates.

Perhaps one of the most exciting crystalline-driven effect that can be exploited is

topological order due to the possibility to achieve backscattering-immune, Robust, Or non-reciprocal waveguiding.

However, solid-state experiments only provide a limited set of physical systems and probes that can reveal non-trivial

topological order. It is thus appealing to seek for alternative setups exhibiting topological properties.

We will investigate the behavior of fermionic matter under strong gauge fields in order to study quantum Hall physics and the emergence of

topological order in a fully tunable experimental geometry.

Of particular interest is the prediction of emergent behaviour in many-body systems - the way in which many particles conspire together to create unexpected and fascinating phenomena such as superconductivity and unconventional phases involving

topological order. This project will develop advanced numerical techniques based on understanding quantum information in many-body systems, and apply these techniques to prototypical models and recently developed analogue quantum simulators that allow for direct implementation in a flexible, experimental setting."