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Dynamically reduced spaces in condensed matter physics:
Quantum Hall bilayers, dimensional reduction, and magnetic spin systems

Abstract : For a description of the low-temperature physics of condensed-matter systems, it is often useful to work within dynamically reduced spaces. This philosophy equally applies to quantum Hall bilayer systems, anyon systems, and frustrated magnetic spin systems - three examples studied in this thesis.

First, we developed a new class of wave functions based upon paired composite fermions. These were applied to analyze the physics of the quantum Hall bilayer system at total filling one. Studying these via variational Monte Carlo methods, we concluded that the compressible to incompressible transition in the bilayer system is of second order. Furthermore, we pursued the longstanding question of whether pairing in the single layer might cause an incompressible quantum state at half filling. We then considered schemes of dimensional reduction for quantum mechanical models on the sphere. We achieved a mapping from non-interacting particles on the sphere to free particles on the circle. We proposed that an analogous mapping might exist for interacting anyons, and an appropriate anyon-like model on the sphere was introduced. Lastly, we performed an analysis of magnetic spin systems on two-dimensional lattices addressing the question of whether spin-ice can be realized in the presence of long-range dipolar interactions.
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Submitted on : Thursday, December 21, 2006 - 7:50:31 PM
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Gunnar Möller. Dynamically reduced spaces in condensed matter physics:
Quantum Hall bilayers, dimensional reduction, and magnetic spin systems. Condensed Matter [cond-mat]. Université Paris Sud - Paris XI, 2006. English. ⟨tel-00121765⟩

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