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

Ihrig, Bernhard; Janssen, Lukas; Mihaila, L.; Scherer, Michael M.

doi:10.1103/physrevb.98.115163

Cited by 33 publications

(34 citation statements)

References 83 publications

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“…However, at smaller values of N f there is a discernible deviation amongst the various Padé approximants. A similar phenomenon was apparent for the chiral Ising QED-GNY theory [19,26] as well as for pure QED [17], whereas Padé approximants for pure GNY models are comparatively better behaved [46,57,72]. Physically this can be understood from the fact that the disordered phase of pure GNY models (a Dirac semimetal) is adiabatically connected to a system of noninteracting Dirac fermions regardless of the value of N f , whereas in QED-GNY models the disordered phase (the ASL) consists of a system of mutually interacting Dirac fermions and gauge fields which becomes increasingly strongly coupled in the infrared for small N f (at least in the sense of the 1/N f expansion).…”

Section: A Chiral Heisenberg Qed3-gny Modelsupporting

confidence: 67%

Critical properties of the Néel–algebraic-spin-liquid transition

et al. 2019

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The algebraic spin liquid is a long-sought-after phase of matter characterized by the absence of quasiparticle excitations, a low-energy description in terms of emergent Dirac fermions and gauge fields interacting according to (2+1)D quantum electrodynamics (QED3), and power-law correlations with universal exponents. The prototypical algebraic spin liquid is the Affleck-Marston π-flux phase, originally proposed as a possible ground state of the spin-1/2 Heisenberg model on the 2D square lattice. While the latter model is now known to order antiferromagnetically at zero temperature, recent sign-problem-free quantum Monte Carlo simulations of spin-1/2 fermions coupled to a compact U (1) gauge field on the square lattice have shown that quantum fluctuations can destroy Néel order and drive a direct quantum phase transition to the π-flux phase. We show this transition is in the universality class of the chiral Heisenberg QED3-Gross-Neveu-Yukawa model with a single SU (2) doublet of four-component Dirac fermions (i.e., N f = 1), pointing out important differences with the corresponding putative transition on the kagomé lattice. Using an expansion below four spacetime dimensions to four-loop order, and a large-N f expansion up to second order, we show the transition is continuous and compute various thermodynamic and susceptibility critical exponents at this transition, setting the stage for future numerical determinations of these quantities. As a byproduct of our analysis, we also obtain charge-density-wave and valence-bond-solid susceptibility exponents at the semimetal-antiferromagnetic insulator transition in graphene. arXiv:1905.03719v1 [cond-mat.str-el]

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Section: A Chiral Heisenberg Qed3-gny Modelsupporting

confidence: 67%

Critical properties of the Néel–algebraic-spin-liquid transition

et al. 2019

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“…Looking forward, better algorithm in QMC simulations would certainly be desirable to access larger system sizes and lower temperatures. In particular, the critical properties of the U1D-VBS transition, that of the QED 3 -GN types, have already been discussed in the high-order perturbative RG calculations [42][43][44][45], but the system sizes in this work is too small to extract accurate values of the critical exponents. Further developments, in terms of algorithm improvement and more focus close to the QED 3 -GN critical points, are on-going.…”

Section: Conclusion and Discussionmentioning

confidence: 95%

“…The gapless excitation close to (π, 0) are the critical fluctuations associated with the QED 3 -GN transition. With larger system sizes and lower temperature in the future QMC studies, one will be able to measure the anomalous dimension exponent η from the momentum and frequency dependence of such critical fluctuation, and could compare with the predictions of QED 3 -GN transitions from the recent perturbative RG calculations [42][43][44][45].…”

Section: Dimer Spectra In Uid and Vbs Phasesmentioning

confidence: 99%

“…[1], there are recently several analytical works addressing the critical properties of them [42][43][44][45][46][47]. And the conclusions drawn there are that the U(1)-to-AFM and U(1)-to-VBS phase transitions are indeed possible and the higher-order perturbative RG calculations performed also suggest the possible range of critical exponents of these QED 3 -GN transitions within 1/N f and 4 − expansions [42][43][44][45][46][47].…”

Section: Introductionmentioning

confidence: 96%

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Dynamics of compact quantum electrodynamics at large fermion flavor

Wang

et al. 2019

Phys. Rev. B

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Thanks to the development in quantum Monte Carlo technique, the compact U(1) lattice gauge theory coupled to fermionic matter at (2+1)D is now accessible with large-scale numerical simulations, and the ground state phase diagram as a function of fermion flavor (N f ) and the strength of gauge fluctuations is mapped out [1]. Here we focus on the large fermion flavor case (N f = 8) to investigate the dynamic properties across the deconfinement-to-confinement phase transition. In the deconfined phase, fermions coupled to the fluctuating gauge field to form U(1) spin liquid with continua in both spin and dimer spectral functions, and in the confined phase fermions are gapped out into valence bond solid phase with translational symmetry breaking and gapped spectra. The dynamical behaviors provide supporting evidence for the existence of the U(1) deconfined phase and could shine light on the nature of the U(1)-to-VBS phase transition which is of the QED 3 -Gross-Neveu chiral O(2) universality whose properties still largely unknown.

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“…The continuous confined transitions from U1D to AFM or VBS we found should be described by QED 3 -Gross-Neveu O (2) or O(3) universality, depending on the symmetry group that the fermion bilinears break in the confined phase, and further carefully study of the critical properties of these transitions via QMC simulations and analytical calculations is certainly worthwhile [93]. Recently perturbative renormalization group calculations to higher orders have been carried out in attempt to accquire the critical properties of the deconfinement to confinement transition in form of QED 3 -Gross-Neveu universality classes [120][121][122][123][124][125] and to address the relevance or irrelevance of the monopole operators to the stability of the U1D phase [126][127][128], show substantial interests and great ongoing efforts along this direction.…”

Section: A Dirac Fermions Coupled With Phononsmentioning

confidence: 99%

Revealing fermionic quantum criticality from new Monte Carlo techniques

Liu

Pan

et al. 2019

J. Phys.: Condens. Matter

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This review summarizes recent developments in the study of fermionic quantum criticality, focusing on new progress in numerical methodologies, especially quantum Monte Carlo methods, and insights that emerged from recently large-scale numerical simulations. Quantum critical phenomena in fermionic systems have attracted decades of extensive research efforts, partially lured by their exotic properties and potential technology applications and partially awaked by the profound and universal fundamental principles that govern these quantum critical systems. Due to the complex and non-perturbative nature, these systems belong to the most difficult and challenging problems in the study of modern condensed matter physics, and many important fundamental problems remain open. Recently, new developments in model design and algorithm improvements enabled unbiased large-scale numerical solutions to be achieved in the close vicinity of these quantum critical points, which paves a new pathway towards achieving controlled conclusions through combined efforts of theoretical and numerical studies, as well as possible theoretical guidance for experiments in heavy-fermion compounds, Cu-based and Fe-based superconductors, ultra-cold fermionic atomic gas, twisted graphene layers, etc., where signatures of fermionic quantum criticality exist. CONTENTS

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

Cited by 33 publications

References 83 publications

Critical properties of the Néel–algebraic-spin-liquid transition

Critical properties of the Néel–algebraic-spin-liquid transition

Dynamics of compact quantum electrodynamics at large fermion flavor

Revealing fermionic quantum criticality from new Monte Carlo techniques

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