Symmetry and Topological Order

We prove sufficient conditions for Topological Quantum Order at both zero and finite temperatures. The crux of the proof hinges on the existence of low-dimensional Gauge-Like Symmetries (that notably extend and differ from standard local gauge symmetries) and their associated defects, thus providing a unifying framework based on a symmetry principle. These symmetries may be actual invariances of the system, or may emerge in the low-energy sector. Prominent examples of Topological Quantum Order display Gauge-Like Symmetries. New systems exhibiting such symmetries include Hamiltonians depicting orbital-dependent spin exchange and Jahn-Teller effects in transition metal orbital compounds, short-range frustrated Klein spin models, and p+ip superconducting arrays. We analyze the physical consequences of Gauge-Like Symmetries (including topological terms and charges), discuss associated braiding, and show the insufficiency of the energy spectrum, topological entanglement entropy, maximal string correlators, and fractionalization in establishing Topological Quantum Order. General symmetry considerations illustrate that not withstanding spectral gaps, thermal fluctuations may impose restrictions on certain suggested quantum computing schemes and lead to "thermal fragility". Our results allow us to go beyond standard topological field theories and engineer systems with Topological Quantum Order.Comment: 10 pages, 2 figures. Minimal changes relative to published version- most notably the above shortened title (which was too late to change upon request in the galley proofs). An elaborate description of all of the results in this article appeared in subsequent works, principally in arXiv:cond-mat/0702377 which was published in the Annals of Physics 324, 977- 1057 (2009

Real time multimodal interaction with animated virtual human

This paper describes the design and implementation of a real time animation framework in which animated virtual human is capable of performing multimodal interactions with human user. The animation system consists of several functional components, namely perception, behaviours generation, and motion generation. The virtual human agent in the system has a complex underlying geometry structure with multiple degrees of freedom (DOFs). It relies on a virtual perception system to capture information from its environment and respond to human user's commands by a combination of non-verbal behaviours including co-verbal gestures, posture, body motions and simple utterances. A language processing module is incorporated to interpret user's command. In particular, an efficient motion generation method has been developed to combines both motion captured data and parameterized actions generated in real time to produce variations in agent's behaviours depending on its momentary emotional states