Fermionic quantum criticality in honeycomb and<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>π</mml:mi></mml:math>-flux Hubbard models: Finite-size scaling of renormalization-group-invariant observables from quantum Monte Carlo

Toldin, Francesco Parisen; Hohenadler, Martin; Assaad, Fakher F.; Herbut, Igor F.

doi:10.1103/physrevb.91.165108

Cited by 194 publications

(199 citation statements)

References 49 publications

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“…By extrapolating the magnetization to the thermodynamical limit, Ref. [1] located the critical point at U/t = 3.78, a value in line with recent numerical simulations [75,76]. According to the present study, the pinning field is a relevant perturbation for the line critical behavior, so that for h 0 = 0, under the RG the model flows away from the "ordinary" fixed point h 0 = 0.…”

Section: Discussion and Future Directionssupporting

confidence: 87%

Critical behavior in the presence of an order-parameter pinning field

2017

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We apply a recently advocated simulation scheme that employs a local order-parameter pinning field to study quantum critical phenomena in the two-dimensional square-lattice bilayer quantum Heisenberg model. Using a world-line quantum Monte Carlo approach, we show that for this model, the pinning-field approach allows to locate the quantum critical point over a wide range of pinning-field strengths. However, the identification of the quantum critical scaling behavior is found to be hard since the pinning field introduces strong corrections to scaling. In order to further elucidate the scaling behavior in this situation, we also study an improved classical lattice model in the three-dimensional Ising universality class by means of Monte Carlo simulations on large lattice sizes, which allow us to employ refined finite-size scaling considerations. A renormalization group analysis exhibits the presence of an important crossover effect from the zero pinning-field to a critical adsorption fixed point. In line with field-theoretical results, we find that at the critical adsorption fixed point the shortdistance expansion of the order-parameter profile exhibits a new universal critical exponent. This result also implies the presence of slowly decaying scaling corrections, which we analyze in detail.

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Section: Discussion and Future Directionssupporting

confidence: 87%

Critical behavior in the presence of an order-parameter pinning field

2017

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“…One possible origin of the differences might be effects from corrections to scaling [96,97] at least when it comes to the comparison between the renormalization group and the lattice methods. For example, a close to marginal scaling of the difference between the boson and fermion velocities which is generally nonvanishing in the lattice approaches could be difficult to assess and have a strong impact on the fitting procedure of the appropriate scaling functions.…”

Section: Discussionmentioning

confidence: 99%

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

et al. 2017

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We study the chiral Ising, the chiral XY, and the chiral Heisenberg models at four-loop order with the perturbative renormalization group in 4 − ϵ dimensions and compute critical exponents for the GrossNeveu-Yukawa fixed points to order Oðϵ 4 Þ. Further, we provide Padé estimates for the correlation length exponent, the boson and fermion anomalous dimension, as well as the leading correction to scaling exponent in 2 þ 1 dimensions. We also confirm the emergence of supersymmetric field theories at four loops for the chiral Ising and the chiral XY models with N ¼ 1=4 and N ¼ 1=2 fermions, respectively. Furthermore, applications of our results relevant to various quantum transitions in the context of Dirac and Weyl semimetals are discussed, including interaction-induced transitions in graphene and surface states of topological insulators.

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“…Such quantum critical behaviors at low energy may be described by the Gross-Neveu [9] or Gross-Neveu-Yukawa theory which has been studied in graphene [10][11][12][13], in d-wave nodal superconductors [14][15][16][17], as well as in high-energy physics [18][19][20][21] using various RG approaches such as large-N and dimensional regularization. Numerical methods such as quantum Monte Carlo simulations [22][23][24][25][26] have also been employ to study this type of quantum critical behavior in lattice models [27][28][29][30][31][32]. Nonetheless, critical exponents obtained in RG calculations are often in discrepancy with the ones from QMC calculations of lattice models when QMC simulations encounter the notorious fermion-sign-problem [33,34] or when N is small.…”

Section: Introductionmentioning

confidence: 99%

Fermion-sign-free Majarana-quantum-Monte-Carlo studies of quantum critical phenomena of Dirac fermions in two dimensions

2015

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Quantum critical phenomena may be qualitatively different when massless Dirac fermions are present at criticality. Using our recently-discovered fermion-sign-free Majorana quantum Monte Carlo method introduced by us in (Li et al 2015 Phys. Rev. B 91 241117), we investigate the quantum critical phenomena of spinless Dirac fermions at their charge-density-wave phase transitions on the honeycomb lattice having N L 2 s 2 = sites with largest L = 24. By finite-size scaling, we accurately obtain critical exponents of this so-called Gross-Neveu chiral-Ising universality class of two (twocomponent) Dirac fermions in 2+1D: 0.45(2) η = , 0.77(3) ν = , and 0.60(3) β =, which are qualitatively different from the mean-field results but are reasonably close to the ones obtained from renormalization group calculations.

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Fermionic quantum criticality in honeycomb andπ-flux Hubbard models: Finite-size scaling of renormalization-group-invariant observables from quantum Monte Carlo

Cited by 194 publications

References 49 publications

Critical behavior in the presence of an order-parameter pinning field

Critical behavior in the presence of an order-parameter pinning field

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

Fermion-sign-free Majarana-quantum-Monte-Carlo studies of quantum critical phenomena of Dirac fermions in two dimensions

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