Ultra-cold fermions in optical lattices

We summarize recent theoretical results for the signatures of strongly correlated ultra-cold fermions in optical lattices. In particular, we focus on collective mode calculations, where a sharp decrease in collective mode frequency is predicted at the onset of the Mott metal-insulator transition; and correlation functions at finite temperature, where we employ a new exact technique that applies the stochastic gauge technique with a Gaussian operator basis.

Automated layout of small lattices using layer diagrams

Good quality concept lattice drawings are required to effectively communicate logical structure in Formal Concept Analysis. Data analysis frameworks such as the Toscana System use manually arranged concept lattices to avoid the problem of automatically producing high quality lattices. This limits Toscana systems to a finite number of concept lattices that have been prepared a priori. To extend the use of formal concept analysis, automated techniques are required that can produce high quality concept lattice drawings on demand. This paper proposes and evaluates an adaption of layer diagrams to improve automated lattice drawing. © Springer-Verlag Berlin Heidelberg 2006.

Drinfeld twists and algebraic bethe ansatz of the supersymmetric model associated with U-q(gl(m vertical bar n))

We construct the Drinfeld twists (or factorizing F-matrices) of the supersymmetric model associated with quantum superalgebra U-q(gl(m vertical bar n)), and obtain the completely symmetric representations of the creation operators of the model in the F-basis provided by the F-matrix. As an application of our general results, we present the explicit expressions of the Bethe vectors in the F-basis for the U-q(gl(2 vertical bar 1))-model (the quantum t-J model).