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+σ 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 σ-d plane shows a nontrivial dependence on σ. As a consequence of the fact that the model is quantum, the correlation functions are 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 criticality. Results for the correlation length exponent ν, 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. [10.1103/PhysRevB.96.104432]

Criticality and phase diagram of quantum long-range O(N) models

Defenu, Nicolò;Trombettoni, Andrea;Ruffo, Stefano
2017

Abstract

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+σ 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 σ-d plane shows a nontrivial dependence on σ. As a consequence of the fact that the model is quantum, the correlation functions are 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 criticality. Results for the correlation length exponent ν, the dynamical critical exponent z, and a comparison with numerical findings for them are presented.
96
10
1
11
104432
http://harvest.aps.org/v2/bagit/articles/10.1103/PhysRevB.96.104432/apsxml
https://arxiv.org/abs/1704.00528
Defenu, Nicolò; Trombettoni, Andrea; Ruffo, Stefano
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11767/71194
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