Four-loop critical exponents for the Gross-Neveu-Yukawa models

Zerf, Nikolai; Herbut, Igor F.; Scherer, Michael M.; Marquard, Peter; Mihaila, L.

doi:10.1103/physrevd.96.096010

Cited by 164 publications

(312 citation statements)

References 103 publications

(225 reference statements)

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“…These exponents are related to the slopes of the beta functions in the critical GNY model. Our results are in complete agreement with the expressions for the perturbative four loop beta functions in the GNY model obtained recently in [19]. For the calculation we used the method developed in [21][22][23].…”

Section: Discussionsupporting

confidence: 76%

“…The results available from 1/N expansion provide an additional check for the perturbative calculations. The four loop RG functions obtained in [19] are in a perfect agreement with the results of 1/N calculations [3][4][5][6][7][8][9]. In this paper we present 1/N 2 expressions for the other two indices -the so-called correction exponents that are related to the slopes of β functions at the critical point and were known only with 1/N accuracy [20].…”

Section: Introductionsupporting

confidence: 70%

“…Moreover, the chiral extension of the GNY model -the Nambu-JonaLasinio (NJL) model -describes, for a low number of fermion a e-mail: alexander.manashov@desy.de b e-mail: matthias.strohmaier@ur.de flavors, a system with an emergent supersymmetry [16]. The recent calculation of the corresponding renormalization group (RG) functions with four-loop accuracy [17][18][19] confirms the emergence of supersymmetry at the critical point.…”

Section: Introductionmentioning

confidence: 86%

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Correction exponents in the Gross–Neveu–Yukawa model at $$1/N^2$$ 1 / N 2

Manashov

Strohmaier

2018

Eur. Phys. J. C

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Section: Discussionsupporting

confidence: 76%

Section: Introductionsupporting

confidence: 70%

Section: Introductionmentioning

confidence: 86%

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Correction exponents in the Gross–Neveu–Yukawa model at $$1/N^2$$ 1 / N 2

Manashov

Strohmaier

2018

Eur. Phys. J. C

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“…(15) and (16) generalize previous results for the chiral Ising, XY, and Heisenberg universality classes 24,28 to the chiral O(N ) universality classes with arbitrary N ∈ N.…”

Section: 2728supporting

confidence: 83%

Compatible orders and fermion-induced emergent symmetry in Dirac systems

Janssen¹,

Herbut²,

Scherer³

2018

Phys. Rev. B

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We study the quantum multicritical point in a (2+1)D Dirac system between the semimetallic phase and two ordered phases that are characterized by anticommuting mass terms with O(N1) and O(N2) symmetry, respectively. Using expansion around the upper critical space-time dimension of four, we demonstrate the existence of a stable renormalization-group fixed point, enabling a direct and continuous transition between the two ordered phases directly at the multicritical point. This point is found to be characterized by an emergent O(N1 + N2) symmetry for arbitrary values of N1 and N2 and fermion flavor numbers N f , as long as the corresponding representation of the Clifford algebra exists. Small O(N )-breaking perturbations near the chiral O(N ) fixed point are therefore irrelevant. This result can be traced back to the presence of gapless Dirac degrees of freedom at criticality, and it is in clear contrast to the purely bosonic O(N ) fixed point, which is stable only when N < 3. As a by-product, we obtain predictions for the critical behavior of the chiral O(N ) universality classes for arbitrary N and fermion flavor number N f . Implications for critical Weyl and Dirac systems in (3+1)D are also briefly discussed.Introduction. The interplay and competition of different ordering tendencies in many-body systems are the source of various exciting phenomena, including unconventional superconductivity, the nature of quantum spin liquids, and the physics of deconfined criticality. These notoriously challenging problems sometimes become theoretically accessible when an emergent higher symmetry can be found. The complex phase diagram of the high-T c superconductors, for instance, has been argued to be deducible from an emergent symmetry in which the O(3) Néel and U(1) superconducting order parameters are combined into a five-tuplet which turns out to be a vector under O(5).1 Numerical simulations of the deconfined critical point between the Néel and valence bond solid orders on the square lattice also find evidence for an emergent O(5) symmetry.2 The emergence of this symmetry can be made natural by postulating duality relations between the bosonic gauge theory describing the deconfined critical point and certain fermionic theories.3,4 Similarly, recent quantum Monte Carlo simulations of Dirac fermions in 2 + 1 dimensions find a direct and continuous transition between O(3) and Z 2 ordered phases with an emergent O(4) symmetry at criticality.

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“…We have checked that our β-function agrees at the leading order in N f up to four-loop level by comparing with the result of ref. [19]. Finally, let us comment on the pole structure: the integrand, I 1 (t), has the first pole occuring at t = 3, which results in a logarithmic singularity for F 1 (K) around K = 3.…”

Section: Jhep08(2018)081mentioning

confidence: 99%