Quantum Computation and Information Seminar 

20/06/2006, 14:00 — 15:00 — Room P6, Mathematics Building
Nikola Paunkovic, Instituto Superior Técnico

Ground state overlap, quantum phase transitions and the orthogonality catastrophe

We present a characterization of quantum phase transitions in terms of the the overlap function between two ground states obtained for two different values of external parameters. On the examples of the Dicke and $\mathrm{XY}$ models, we show that the regions of criticality of a system are marked by the extremal points of the overlap and functions closely related to it. Further, we discuss the connections between this approach and the Anderson orthogonality catastrophe as well as its connection with the dynamical study of the Loschmidt echo for critical systems. Joint work with Paolo Zanardi.