Dresden 2009 – scientific programme

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DY: Fachverband Dynamik und Statistische Physik

DY 1: Statistical physics I (general)

DY 1.9: Talk

Monday, March 23, 2009, 12:45–13:00, HÜL 386

Geometric Characterization of Phase Transitions in the Lipkin-Meshkov-Glick Model — •Daniel Scherer, Michael Kastner, and Cord Müller — Physikalisches Institut, Universität Bayreuth, Germany

At least two decades ago people have begun to realize that matter can be macroscopically ordered in ways that do not fit into the framework of the Ginzburg-Landau paradigm for classical degrees of freedom. Since the discoveries of high-temperature superconductivity and the quantum Hall effect, novel aspects such as quantum phase transitions and topological order have become the focus of both theoretical and experimental efforts. On the theoretical side, several quantities have been proposed to trace signatures of such exotic phase transitions and to characterize the physics within those phases. One of these approaches is given by the so called fidelity metric. This is a Riemannian metric on the state space of a quantum system, that might allow for a common description of both Ginzburg-Landau and topological order independently of knowledge, or even existence, of a local order parameter. We apply this approach to the Lipkin-Meshkov-Glick Model exhibiting conventional (Ginzburg-Landau) order at finite temperature. We obtain the fidelity metric for ordered and disordered phases in the isotropic model and show that in this case the metric can be expressed completely in terms of the free energy. Finally we point out similarities with Ruppeiner geometry.