Weak solution of the non-perturbative renormalization group equation to describe dynamical chiral symmetry breaking

Aoki, Kenichi; Kumamoto, Shin-Ichiro; Sato, Daisuke

doi:10.1093/ptep/ptu039

Cited by 20 publications

(27 citation statements)

References 14 publications

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“…If T * < T 0 then the system is in the symmetry broken phase and the shock size at final time T 0 gives the value of the order parameter. A similar mechanism was recently proposed for the chiral symmetry breaking transition in the 4D Nambu-Jona-Lasinio model [47].…”

Section: Large N Limit and Burgers Equationsupporting

confidence: 65%

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Disorder-Driven Quantum Transition in Relativistic Semimetals: Functional Renormalization via the Porous Medium Equation

2018

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In the presence of randomness, a relativistic semimetal undergoes a quantum transition towards a diffusive phase. A standard approach relates this transition to the U (N ) Gross-Neveu model in the limit of N → 0. We show that the corresponding fixed point is infinitely unstable, demonstrating the necessity to include fluctuations beyond the usual Gaussian approximation. We develop a functional renormalization group method amenable to include these effects and show that the disorder distribution renormalizes following the so-called porous medium equation. We find that the transition is controlled by a nonanalytic fixed point drastically different from that of the U (N ) Gross-Neveu model. Our approach provides a unique mechanism of spontaneous generation of a finite density of states and also characterizes the scaling behavior of the broad distribution of fluctuations close to the transition. It can be applied to other problems where nonanalytic effects may play a role, such as the Anderson localization transition.Introduction. -The interplay between disorder and quantum fluctuations leads to unique phenomena, the most remarkable being the Anderson localization. After more than half a century of intensive efforts, it remains a topical subject of research with applications to various domains of physics ranging from condensed matter to cold atoms and light propagation [1]. Remarkably, a different type of disorder-driven quantum phase transition was discovered recently when considering waves with a quantum relativistic dispersion relation [2]. This transition happens between a pseudoballistic phase and a diffusive metal as a function of the disorder strength (or the energy). It is predicted to occur in particular in the recently discovered three-dimensional (3D) Weyl [3,4] and Dirac semimetals [5][6][7] in which, respectively, two and four electronic bands cross linearly at isolated points. However we expect these phenomena to be relevant to other relativistic waves beyond condensed matter, such as ultracold atoms [8].In spite of numerous efforts, the understanding of this transition remains elusive. In this Letter we show that the fluctuations of the randomness beyond the standard Gaussian approximation invalidate previous fieldtheoretic descriptions of this transition. A very similar mechanism occurs in the context of the Anderson transition: there discrepancies between the results obtained using renormalization group (RG) and numerical simulations grow with the number of loops [9]. One may attribute them to the existence of infinitely many relevant operators of the associated field theory [10] which destabilize the fixed point (FP) usually considered to describe the transition [11][12][13]. We find that the same problem appears at the new semimetal-diffusive metal transition. We demonstrate how to overcome this obstacle by deriving and solving a functional renormalization group (FRG) for the whole (non-Gaussian) disorder distribution. To our knowledge this solution consti-tutes the only example of an analytical de...

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Section: Large N Limit and Burgers Equationsupporting

confidence: 65%

“…Any strong solution is also a weak solution but not vice versa. A weak solution to the FRG equation can exist and describe infrared physical quantities even when the flow equation does not have a strong solution [47]. The same arguments are also applied to the PME [33].…”

Section: Weak Vs Strong Solutionmentioning

confidence: 96%

Disorder-Driven Quantum Transition in Relativistic Semimetals: Functional Renormalization via the Porous Medium Equation

2018

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“…Some of its most important applications in the history of physics are the elimination of ultraviolet divergences in renormalizable quantum field theories and its application to explain the universality properties of continuous phase transitions. The FRG has been extensively used to study the QCD phase diagram using chiral effective models beyond the MF, like the NJL model [34][35][36][37] and the QM model [38][39][40][41][42][43][44]. For detailed reviews on the FRG method see [45][46][47].…”

Section: Introductionmentioning

confidence: 99%

Functional renormalization group study of the critical region of the quark-meson model with vector interactions

2020

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The critical region of the two flavour quark-meson model with vector interactions is explored using the Functional Renormalization Group, a non-perturbative method that takes into account quantum and thermal fluctuations. Special attention is given to the low temperature and high density region of the phase diagram, which is very important to construct the equation of state of compact stars. As in previous studies, without repulsive vector interaction, an unphysical region of negative entropy density is found near the first order chiral phase transition. We explore the connection between this unphysical region and the chiral critical region, especially the first order line and spinodal lines, using also different values for vector interactions. We find that the unphysical negative entropy density region appears because the $$s=0$$s=0 isentropic line, near the critical region, is displaced from its $$T=0$$T=0 location. For certain values of vector interactions this region is pushed to lower temperatures and high chemical potentials in such way that the negative entropy density region on the phase diagram can even disappear. In the case of finite vector interactions, the location of the critical end point has a non-trivial behaviour in the $$T-\mu _B$$T-μB plane, which differs from that in mean field calculations.

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“…The FRG has been applied to the NJL model with a scale dependence incorporated in the four-Fermi interaction coupling. However, such a scheme leads to a diverging coupling in the renormalization group flow, that signals spontaneous breaking of chiral symmetry, for more information see [42][43][44]. Recently, different schemes have been used to apply the FRG to a theory with four-Fermi interactions, like the NJL model, see [42][43][44][45][46].…”

Section: Introductionmentioning

confidence: 99%

One-meson-loop NJL model: Effect of collective and noncollective excitations on the quark condensate at finite temperature

Pereira

Costa

2020

Phys. Rev. D

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We explore the effect of including quantum fluctuations in the two flavor Nambu−Jona-Lasinio model at finite temperature. This is accomplished, in a symmetry preserving way, by including collective and noncollective modes in the one-meson-loop gap equation which originate from poles and branch cuts in the complex plane, respectively. The inclusion of a boson cutoff, Λ b , is necessary to regularize the meson-loop momenta. This new parameter is used to study the influence of going beyond the usual mean field approximation in the quark condensate. As the temperature increases, chiral symmetry tends to get restored, the collective modes melt and only noncollective modes contribute to the quark condensate. With the inclusion of such modes, the quark condensate at finite temperature has a different behavior than at mean field level that will be explored. * renan.pereira@student.uc.pt † pcosta@uc.pt arXiv:2003.08430v1 [hep-ph]

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Weak solution of the non-perturbative renormalization group equation to describe dynamical chiral symmetry breaking

Cited by 20 publications

References 14 publications

Disorder-Driven Quantum Transition in Relativistic Semimetals: Functional Renormalization via the Porous Medium Equation

Disorder-Driven Quantum Transition in Relativistic Semimetals: Functional Renormalization via the Porous Medium Equation

Functional renormalization group study of the critical region of the quark-meson model with vector interactions

One-meson-loop NJL model: Effect of collective and noncollective excitations on the quark condensate at finite temperature

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