Seminar by Nikola Paunkovic

SCL hosted a seminar by Dr. Nikola Paunkovic from the Instituto de TelecomunicaƧƵes, Lisbon, Portugal on 29 December 2009. In the seminar talk entitled "Macroscopic Distinguishability Between Quantum States Defining Different Phases of Matter", Dr. Paunkovic presented a new, quantum-information-inspired method for characterization of phase transitions.

Abstract of the talk:
We show that fidelity, a measure of state distinguishability, used in quantum information, can be efficiently employed as a tool to detect some macroscopic phase transitions and we establish its relation to standard many-body properties.

In the case of quantum phase transitions, we show, on the examples of the Dicke and the XY models, that approaching the regions of criticality the fidelity between two neighboring ground states exhibits a dramatic drop.

In the case of general thermal phase transitions, we make the analytical study of the Hubbard-Stoner model of itinerant magnetism and the BCS model of superconductivity, showing that the sudden drop of the mixed state fidelity between two neighboring global thermal states marks the line of the phase transition. We conduct a detailed analysis of the general case of systems given by mutually commuting Hamiltonians, where the non-analyticity of the fidelity is directly related to the non-analyticity of the relevant response functions (susceptibility and heat capacity), for the case of symmetry-breaking transitions. Further, on the case of BCS theory of superconductivity, given by mutually non commuting Hamiltonians, we analyze the structure of the system`s eigenvectors in the vicinity of the line of the phase transition showing that their sudden change is quantified by the emergence of a generically non-trivial Uhlmann mixed state geometric phase, the mixed-state generalization of the Berry geometric phase.

Finally, we make the numerical study of an impurity in a superconductor film, and look at the fidelity between partial (either one-site or two-site) quantum states, observing a sudden drop of the fidelity between two partial states corresponding either to the impurity location or its close vicinity.

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