Several recent experiments in atomic, molecular, and optical systems motivated a huge interest in the study of quantum long-range 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+Ï 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 Ï-d plane shows a nontrivial dependence on Ï. As a consequence of the fact that the model is quantum, the correlation functions are anisotropic in the spatial and time coordinates for Ï smaller than a critical value, and in this region the isotropy is not restored even at criticality. Results for the correlation length exponent Î½, the dynamical critical exponent z, and a comparison with numerical findings for them are presented.
Criticality and phase diagram of quantum long-range O(N) models / Defenu, Nicolò; Trombettoni, Andrea; Ruffo, Stefano. - In: PHYSICAL REVIEW. B. - ISSN 2469-9950. - 96:10(2017), pp. 1-11.
|Titolo:||Criticality and phase diagram of quantum long-range O(N) models|
|Autori:||Defenu, Nicolò; Trombettoni, Andrea; Ruffo, Stefano|
|Data di pubblicazione:||2017|
|Numero di Articolo:||104432|
|Digital Object Identifier (DOI):||http://dx.doi.org/10.1103/PhysRevB.96.104432|
|Appare nelle tipologie:||1.1 Journal article|