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

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+...

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Bibliographic Details
Main Authors: Defenu, Nicolò (Author) , Trombettoni, Andrea (Author) , Ruffo, Stefano (Author)
Format: Article (Journal)
Language:English
Published: 22 September 2017
In: Physical review
Year: 2017, Volume: 96, Issue: 10
ISSN:2469-9969
DOI:10.1103/PhysRevB.96.104432
Online Access:Verlag, Volltext: http://dx.doi.org/10.1103/PhysRevB.96.104432
Verlag, Volltext: https://link.aps.org/doi/10.1103/PhysRevB.96.104432
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Author Notes:Nicolò Defenu, Andrea Trombettoni, and Stefano Ruffo
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Summary: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.
Item Description:Gesehen am 12.03.2018
Physical Description:Online Resource
ISSN:2469-9969
DOI:10.1103/PhysRevB.96.104432

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