Criticality and Phase Diagram of Quantum Long-Range $\text{O(N)}$ models

Understand

Several recent experiments in atomic, molecular and optical systems motivated a huge interest in the study of quantum long-range %spin systems.

• Our goal in this paper is to present a general description of their critical behavior and phases, devising a treatment valid in $d$ dimensions, with an exponent $d+\sigma$ for the power-law decay of the couplings in the presence of an $O(N)$ symmetry.
• By introducing a convenient ansatz for the effective action, we 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 $\sigma-d$ plane shows a non trivial dependence on $\sigma$.