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

Defenu, Nicoló; Trombettoni, Andrea; Ruffo, Stefano

doi:10.1103/physrevb.96.104432

Cited by 105 publications

(193 citation statements)

References 60 publications

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“…This is consistent with the results of [64] where it has been shown that for 3  a the phase transition is in the universality class of the SR Ising transition, see also [85,91]. Actually, taking into account corrections beyond mean-field, the threshold for the onset of the SR universality class can be put at α=2.75 [89,106,107].…”

Section: Scaling Along the Fm Critical Linesupporting

confidence: 90%

Multipartite-entanglement tomography of a quantum simulator

2019

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Multipartite-entanglement tomography, namely the quantum Fisher information (QFI) calculated with respect to different collective operators, allows to fully characterize the phase diagram of the quantum Ising chain in a transverse field with variable-range interaction. In particular, it recognizes the phase stemming from long-range (LR) antiferromagnetic interaction, a capability also shared by the spin squeezing. Furthermore, the QFI locates the quantum critical points, both with vanishing and nonvanishing mass gap. In this case, we also relate the finite-size power-law exponent of the QFI to the critical exponents of the model, finding a signal for the breakdown of conformal invariance in the deep LR regime. Finally, the effect of a finite temperature on the multipartite entanglement, and ultimately on the phase stability, is considered. In light of the current realizations of the model with trapped ions and of the potential measurability of the QFI, our approach yields a promising strategy to probe LR physics in controllable quantum systems.

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Section: Scaling Along the Fm Critical Linesupporting

confidence: 90%

Multipartite-entanglement tomography of a quantum simulator

2019

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“…The present FRG approach has the indisputable advantage to capture, within a single calculation a consistent picture for the SSB transition in the whole d, σ and N parameter space, as a down side the topological phase transition which shall occur for σ = 2 in d = 1 can only be addressed within the present formalism [117]. In passing we note that the MC results for a quantum XY model coupled to an anomalous Bosonic bath [118] seem to provide a value σ * = 2 − η with η = 1 4 even for the N = 2, which is consistent with the BKT scenario [see [119] for a recent numerical study of the dilute LR XY model].…”

Section: The Critical Exponentsmentioning

confidence: 99%

“…In this work, we deal with the previous issues by first considering the case of classical O(N ) models in dimension d ≥ 2 for weak LR interactions, see Sections II-III. The goal of these sections is to review the FRG treatment for classical models and to set up the ground for the study of the quantum case, which is the subject of Sections IV-IV C. Our presentation is based on the formalism developed and the results obtained in [27][28][29], while the presentation follows the one in [30]. Our main objectives is to present such findings in an unified and compact way, providing as well details on the derivations and new results on the topic of weak LR spin systems.…”

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confidence: 99%

Criticality of spin systems with weak long-range interactions

Defenu¹,

Codello²,

Ruffo³

et al. 2020

J. Phys. A: Math. Theor.

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The study of critical properties of systems with long-range interactions has attracted in the last decades a continuing interest and motivated the development of several analytical and numerical techniques, in particular in connection with spin models. From the point of view of the investigation of their criticality, a special role is played by systems in which the interactions are long-range enough that their universality class is different from the short-range case and, nevertheless, they maintain the extensivity of thermodynamical quantities. Such interactions are often called weak long-range. In this paper we focus on the study of the critical behaviour of spin systems with weak-long range couplings using renormalization group, and we review their remarkable properties. For the sake of clarity and self-consistency, we start from the classical O(N ) spin models and we then move to quantum spin systems. I. INTRODUCTIONIn this Special Issue several aspects of the equilibrium and dynamical properties of systems with long-range (LR) interactions are discussed. In the paper we apply concepts and tools developed for LR systems, including the modern renormalization group approach, to the study of spin models with weak LR interactions. Such interactions are able to modify the universal properties of the systems in which they act, but anyway preserve the extensivity of the thermodynamic quantities. Our main goal is to present and apply the formalism of the functional renormalization group (FRG) to weak LR systems and show the capability of the FRG to clarify their critical properties, which are in many cases still unknown and sometimes diffucult to obtain with other approaches.Given the wide framework already presented in the other contributions to this Special Issue, it is not necessary to extensively emphasize that LR interactions play an important and paradigmatic role in the study of many body interacting systems, such as O(N ) symmetric models. Indeed, the importance of LR interactions is motivated by their presence in several systems ranging from plasma physics to astrophysics and cosmology [1,2].In order to understand the typical phenomena occurring in spin models with power-law LR couplings and define the weak LR regime, let us first consider the classical O(N ) symmetric models, whose Hamiltonian reads(1)The spin variables S i are unit vectors with N components, placed at the sites, labeled by the index i, of a d dimensional lattice. The coupling constant J is constant for a decay exponent σ > 0, conversely for σ ≤ 0 the coupling constant J needs to be rescaled by an appropriate power of the system size to absorb the divergence of the interaction energy density the thermodynamic limit [1,2]. When σ > 0 the model may have a second order phase transition. The main result is that three different regimes can occur as a function of the parameter σ [3, 4]:• for σ ≤ d/2 the mean-field approximation correctly describes the universal behavior;• for σ greater than a threshold value, σ * , the model has the same critical...

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“…Then, it would be more convenient to consider different regularization schemes which deliver considerably simpler functional flow equations [33]. Another interesting perspective is the study of the nonunitary family of fixed points generalizing the LPA analysis [34] or long range interacting field theories, both in the classical [35] and quantum case [36,37] or, finally in presence of global symmetries as OðNÞ interactions [8,9,15] or Potts model S nþ1 -symmetries [38]. We leave all these applications to future works.…”

Section: Discussionmentioning

confidence: 99%

Scaling solutions in the derivative expansion

Defenu

Codello

2018

Phys. Rev. D

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Scalar field theories with Z 2 symmetry are the traditional playground of critical phenomena. In this work, these models are studied using functional renormalization group (FRG) equations at order ∂ 2 of the derivative expansion and, differently from previous approaches, the spike plot technique is employed to find the relative scaling solutions in two and three dimensions. The anomalous dimension of the first few universality classes in d ¼ 2 is given, and the phase structure predicted by conformal field theory is recovered (without the imposition of conformal invariance), while in d ¼ 3 a refined view of the standard Wilson-Fisher fixed point is found. Our study enlightens the strength of shooting techniques in studying FRG equations, suggesting them as candidates to investigate strongly nonperturbative theories even in more complex cases.

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

Cited by 105 publications

References 60 publications

Multipartite-entanglement tomography of a quantum simulator

Multipartite-entanglement tomography of a quantum simulator

Criticality of spin systems with weak long-range interactions

Scaling solutions in the derivative expansion

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