Spontaneous breaking of Lorentz symmetry in (
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)-dimensional QED

Janssen, Lukas

doi:10.1103/physrevd.94.094013

Cited by 21 publications

(30 citation statements)

References 106 publications

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“…This result provides another nontrivial crosscheck of our calculations. The power law of the gauge-field propagator at criticality thus reads G A (p) ∝ 1/p exactly, in agreement with the situation in plain QED 3 [58][59][60].…”

Section: A Qed3-gn Modelsupporting

confidence: 77%

“…If indeed existent, any other fixed point would be located outside the perturbative regime for 1 and can only approach the QED 3 -GN fixed point at some finite > 0. Such a fixed-point annihilation scenario is known to oc-cur in various gauge theories both in 2+1D and 3+1D [37,59,[67][68][69][70][71][72], and has recently been entertained also in the context of deconfined criticality in the spin models [4,12]. In this scenario, SO(5) would only emerge as an approximate symmetry near a weakly-first-order phase transition with an exponentially large, but finite correlation length ξ c [73].…”

Section: B Comparison With Duality Predictionsmentioning

confidence: 99%

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Deconfined criticality from the QED3 -Gross-Neveu model at three loops

et al. 2018

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The QED3-Gross-Neveu model is a (2+1)-dimensional U(1) gauge theory involving Dirac fermions and a critical real scalar field. This theory has recently been argued to represent a dual description of the deconfined quantum critical point between Néel and valence bond solid orders in frustrated quantum magnets. We study the critical behavior of the QED3-Gross-Neveu model by means of an expansion around the upper critical space-time dimension of D + c = 4 up to the three-loop order. Estimates for critical exponents in 2 + 1 dimensions are obtained by evaluating the different Padé approximants of their series expansion in . We find that these estimates, within the spread of the Padé approximants, satisfy a nontrivial scaling relation which follows from the emergent SO(5) symmetry implied by the duality conjecture. We also construct explicit evidence for the equivalence between the QED3-Gross-Neveu model and a corresponding critical four-fermion gauge theory that was previously studied within the 1/N expansion in space-time dimensions 2 < D < 4. arXiv:1807.04958v2 [cond-mat.str-el]

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Section: A Qed3-gn Modelsupporting

confidence: 77%

Section: B Comparison With Duality Predictionsmentioning

confidence: 99%

Deconfined criticality from the QED3 -Gross-Neveu model at three loops

et al. 2018

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“…While the infrared fate of QED 3 has extensively been discussed in the last three decades [33][34][35][36][37][38][39][40][41][42][43][44][45], the infrared structure of the QED 3 -GN model has, to the best of our knowledge, not been studied before. In this work, we demonstrate that the QED 3 -GN model exhibits a stable fixed point of the renormalization group (RG) for all fermion flavor numbers N .…”

Section: Introductionmentioning

confidence: 99%

Critical behavior of the QED3 -Gross-Neveu model: Duality and deconfined criticality

Janssen

2017

Phys. Rev. B

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105

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We study the critical properties of the QED3-Gross-Neveu model with 2N flavors of twocomponent Dirac fermions coupled to a massless scalar field and a U(1) gauge field. For N = 1, this theory has recently been suggested to be dual to the SU(2) noncompact CP 1 model that describes the deconfined phase transition between the Néel antiferromagnet and the valence bond solid on the square lattice. For N = 2, the theory has been proposed as an effective description of a deconfined critical point between chiral and Dirac spin liquid phases, and may potentially be realizable in spin-1/2 systems on the kagome lattice. We demonstrate the existence of a stable quantum critical point in the QED3-Gross-Neveu model for all values of N . This quantum critical point is shown to escape the notorious fixed-point annihilation mechanism that renders plain QED3 (without scalar-field coupling) unstable at low values of N . The theory exhibits an upper critical space-time dimension of four, enabling us to access the critical behavior in a controlled expansion in the small parameter = 4 − D. We compute the scalar-field anomalous dimension η φ , the correlation-length exponent ν, as well as the scaling dimension of the flavor-symmetry-breaking bilinearψσ z ψ at the critical point, and compare our leading-order estimates with predictions of the conjectured duality.

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“…In that case, even an infinitely weak coupling flows to the strong coupling regime at low energies, leading to the excitonic pairing instability of the system. This is an efficient way to study dynamical gap generation and has wide applications in QED 3 [143][144][145][146] and 3D quadratic semimetal [43,47]. Moreover, the RG approach also proves to be very powerful in the studies of the impact of shortrange interaction on various phase-transition instabilities in a number of semimetal materials, including 2D Dirac semimetal [147,148], 3D Dirac/Weyl semimetal [149], 3D nodal line semimetal [150,151], and 3D double/tripleWeyl semimetal [152].…”

Section: Lowest Order Truncationmentioning

confidence: 99%

“…Apart from the DS equation approach, one can study dynamical excitonic gap generation by employing other powerful tools, such as RG approach [43,47,87,[143][144][145][146] and Monte Carlo simulation [90][91][92][93][94][95][96][97]. To examine whether a dynamical gap is opened, one could consider all the possible four-fermion couplings, allowed by the lattice symmetry, and study their interplay with the Coulomb interaction.…”

Section: Lowest Order Truncationmentioning

confidence: 99%

Excitonic pairing and insulating transition in two-dimensional semi-Dirac semimetals

Wang¹,

Liu²,

Zhang³

2017

Phys. Rev. B

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A sufficiently strong long-range Coulomb interaction can induce excitonic pairing in gapless Dirac semimetals, which generates a finite gap and drives semimetal-insulator quantum phase transition. This phenomenon is in close analogy to dynamical chiral symmetry breaking in high energy physics. In most realistic Dirac semimetals, including suspended graphene, Coulomb interaction is too weak to open an excitonic gap. The Coulomb interaction plays a more important role at low energies in a two-dimensional semi-Dirac semimetal, in which the fermion spectrum is linear in one component of momenta and quadratic in the other, than a Dirac semimetal, and indeed leads to breakdown of Fermi liquid theory. We study dynamical excitonic gap generation in a two-dimensional semi-Dirac semimetal by solving the Dyson-Schwinger equation, and show that a moderately strong Coulomb interaction suffices to induce excitonic pairing. Additional short-range four-fermion coupling tends to promote excitonic pairing. Among the available semi-Dirac semimetals, we find that TiO2/VO2 nanostructure provides a promising candidate for the realization of excitonic insulator. We also apply the renormalziation group method to analyze the strong coupling between the massless semi-Dirac fermions and the quantum critical fluctuation of excitonic order parameter at the semimetal-insulator quantum critical point, and reveal non-Fermi liquid behaviors of semi-Dirac fermions.

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Spontaneous breaking of Lorentz symmetry in ( 2+ε )-dimensional QED

Cited by 21 publications

References 106 publications

Deconfined criticality from the QED3 -Gross-Neveu model at three loops

Deconfined criticality from the QED3 -Gross-Neveu model at three loops

Critical behavior of the QED3 -Gross-Neveu model: Duality and deconfined criticality

Excitonic pairing and insulating transition in two-dimensional semi-Dirac semimetals

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