Andrea Trombettoni — Università di Trieste #
Criticality and Phase Diagram of Quantum Long-Range Systems #
Several recent experiments in atomic, molecular and optical systems motivated an huge interest in the study of quantum long-range spin systems. The goal of the talk is to present a general description of their critical behavior and phases, devising a treatment valid in d dimensions with an exponent d+σ for the power-law decay of the couplings in the presence of an O(N) symmetry. I will first starting by reminding results on classical long-range systems. Then, by introducing a convenient ansatz for the effective action, one can determine the phase diagram for the N-component quantum rotor model with long-range interactions, with N=1 corresponding to the Ising model. The phase diagram in the σ− d plan shows a non trivial dependence on σ. As a consequence of the fact that the model is quantum, the correlation functions are genuinely strongly anisotropic in the spatial and time coordinates for σ smaller than a critical value and in this region the isotropy is not restored even at the criticality. Results for the correlation length exponent & the dynamical critical exponent and a comparison with numerical findings for them are presented.