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It is shown that the fidelity, a basic notion of quantum information science, may be used to characterize quantum phase transitions, regardless of what type of internal order is present in quantum many-body states. The equivalence between the existence of an order parameter and the orthogonality of different ground-state wavefunctions for a system undergoing a quantum phase transition is used to justify the introduction of the notions of irrelevant and relevant information as the counterparts of fluctuations and orders in the conventional description. The irrelevant and relevant information are quantified, which allows us to identify unstable and stable fixed points (in the sense of renormalization group theory) for quantum spin chains. [ABSTRACT FROM AUTHOR]

Five duality transformations are unveiled for the quantum XYZ model with arbitrary spin in one spatial dimension. The presence of these duality transformations, together with an extra Hamiltonian symmetry, drastically reduce the entire ground-state phase diagram to two finite regimes—the principal regimes, with all the other ten regimes dual to them. Combining with the determination of critical points from the conventional order parameter approach and/or the fidelity approach to quantum phase transitions, we are able to map out the ground-state phase diagram for the quantum XYZ model with arbitrary spin . This is explicitly demonstrated for and 2. As it turns out, all the critical points, with central charge , are self-dual for half-integer as well as integer spin . However, in the latter case, the presence of the Haldane phase results in extra lines of critical points with central charge , which are not self-dual. [ABSTRACT FROM AUTHOR]

We examine the energy surfaces of the driven Rabi model, also known as the biased or generalized Rabi model, as a function of the coupling strength and the driving term. The energy surfaces are plotted numerically from the known analytic solution. The resulting energy landscape consists of an infinite stack of sheets connected by conical intersection points located at the degenerate Juddian points in the eigenspectrum. Trajectories encircling these points are expected to exhibit a nonzero geometric phase. [ABSTRACT FROM AUTHOR]