Dresden 2014 – wissenschaftliches Programm

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TT: Fachverband Tiefe Temperaturen

TT 82: Low-Dimensional Systems: Topological Order (organized by TT)

TT 82.8: Topical Talk

Donnerstag, 3. April 2014, 11:30–12:00, HSZ 204

Density Matrix Renormalization Group: Probing the Topology of Quantum States — •Frank Pollmann — Max-Planck-Institute for the Physics of Complex Systems, Dresden, Germany

Matter occurs in various phases with different properties. Usually these phases are characterized in terms of symmetry breaking. A major discovery in the 1980s was the quantum Hall effect which forms a new kind of ``topological'' order. This order represents exotic phases with unusual properties and cannot be understood in terms of symmetry breaking. Since then, a growing number of instances of topological phases has accumulated, and important applications -- not least topological quantum computers -- have been proposed, but a characterization and classification of these new phenomena has been slow to emerge. In parallel, DMRG has arrived as a powerful numerical method with extensions to two dimensional systems and time-dependent phenomena. I will show how to use DMRG to develop new frameworks that help to understand topologically ordered systems. For example, it is now possible to extract characterizing properties of the anyonic excitations directly from the ground state of fractional quantum Hall systems. This approach further makes contact with ``measurable'' quantities (Hall viscosity) and field theories (central charge at critical points). Other remarkable examples are symmetry protected topological phases in one-dimensional systems for which DMRG provides a complete characterization.