Critical behavior of Dirac fermions from perturbative renormalization

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

doi:10.1103/physrevb.98.125109

Cited by 74 publications

(120 citation statements)

References 117 publications

(270 reference statements)

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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: 66%

“…and the full four-loop result is given in electronic format [58]. Turning finally to the SU (N f ) flavor-adjoint bilinear (83), the four-loop diagrams responsible for the difference (72) in scaling dimensions between the singlet and adjoint bilinears are O(e 2 g 6 ) and vanish for the pure chiral Heisenberg GNY model with e 2 = 0. Thus for the latter model this difference in scaling dimensions can at most be O( 5 ).…”

Section: G Fermion Bilinear Dimensions In the Chiral Heisenberg Gny mentioning

confidence: 99%

“…The use of more sophisticated resummation methods [57] may potentially improve those estimates, but typically requires the introduction of a number of free parameters which effectively adds to the uncertainty. Another potentially beneficial approach to improve exponent estimates in three dimensions is the use of two-and four-dimensional perturbation theory [72]; however, at present there is a lack of two-dimensional studies on the chiral-Heisenberg QED 3 model.…”

Section: A Chiral Heisenberg Qed3-gny Modelmentioning

confidence: 99%

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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: 66%

Section: G Fermion Bilinear Dimensions In the Chiral Heisenberg Gny mentioning

confidence: 99%

Section: A Chiral Heisenberg Qed3-gny Modelmentioning

confidence: 99%

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

et al. 2019

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“…However, unlike the classical case in which the short-time dynamics is completely controlled by a corresponding equilibrium critical point, short-time quantum critical dynamics in an isolated system can also be controlled by a dynamical fixed point, which is similar to a thermal fixed point for a purely bosonic field [52][53][54][55].In the context of equilibrium criticality, gapless Dirac fermions, which appear in various systems including graphene, the surface of topological insulators, and Weyl semimetals, lead to exotic quantum phase transitions [56]. The best known example is the chiral Ising universality class [57][58][59][60], in which the gapless Dirac fermion is coupled to a bosonic field via a Yukawa coupling. However, dynamical phase transitions in these systems have rarely been studied.…”

mentioning

confidence: 99%

“…(3) generates RG processes that renormalize the slow modes, namely, S eff = S 0 + δS,where A > = Dφ > DΨ > DΨ > Ae iS0 denotes the functional integration over fast modes, and the calculation is done to one-loop order.In terms of dimensionless coupling constants,wherecan be understood as the bare scaling dimensions of the coupling constants. ForΩ 0 = 0 + O( ), the RG Eqs (5), and (6) reduce to the corresponding equilibrium ones, giving rise to the usual equilibrium chiral Ising universality class (ECIFP, see e.g., [60]). Also, from Eq.…”

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confidence: 99%

Universal Prethermal Dynamics in Gross-Neveu-Yukawa Criticality

2019

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We study the prethermal dynamics of the Gross-Neveu-Yukawa quantum field theory, suddenly quenched in the vicinity of a quantum critical point. We find that the universal prethermal dynamics is controlled by two fixed points depending on the size of the quench. Besides the usual equilibrium chiral Ising fixed point for a shallow quench, a dynamical chiral Ising fixed point is identified for a deep quench. Intriguingly, the latter is a non-thermal fixed point without any equilibrium counterpart due to the participation of gapless fermionic fields. We also find that in the scaling regime controlled by the equilibrium fixed point, the initial slip exponent is rendered negative if there are enough flavors of fermions, thus providing a unique signature of fermionic prethermal dynamics. We then explore the temporal crossover between the universal scaling regimes governed by the two universality classes. Possible experimental realizations are also discussed.Introduction.-Memory effects are ubiquitous phenomena in nature. The classic example is brain memory in living beings, but memory effects are also widespread in physics. In cosmology, the cosmic microwave background radiation can be regarded as a memory of the Big Bang. In condensed matter physics, memory effects often occur in relaxation dynamics [1,2]. For example, in classical critical systems, the short-time critical dynamics remembers the initial state and affects the critical relaxation process during a macroscopic initial stage [3]. In this stage, the evolution of the system is called the critical initial slip and is characterized by an additional critical exponent, the initial slip exponent [3]. These short-time critical dynamics have been widely exploited in determining the critical point and critical exponents in classical systems [4,5].In the context of isolated quantum systems, a vibrant set of purely quantum memory phenomena have been studied. At long times, quantum chaotic systems are expected to effectively lose memory of their initial state, except for conserved quantities like the total energy. This is encoded in the celebrated eigenstate thermalization hypothesis which states that chaotic energy eigenstates look like equilibrium thermal states of the appropriate temperature [6-10]. However, some long-lived prethermal states, which bring in additional universal initial state information into the dynamics, have been discovered [11][12][13][14][15][16][17]. Various causes for these effects have been proposed, including proximity to integrability [18][19][20][21][22][23], existence of a dynamical phase transition after a global quench [24][25][26][27][28][29][30][31][32][33][34][35], emergence of a non-thermal fixed point [36][37][38][39][40][41][42][43][44][45], nonlocal initial entanglement effects [46,47], and so on. Among these, short-time quantum critical dynamics have recently received considerable attention [48][49][50][51][52][53][54][55]. As with its classical counterpart, a critical initial slip exponent can be defined to characterize the dyna...

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Emergent supersymmetry at large N

Prakash,

Sinha

2024

J. High Energ. Phys.

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We search for infrared fixed points of Gross-Neveu Yukawa models with matrix degrees of freedom in d = 4 − ε. We consider three models — a model with SU(N) symmetry in which the scalar and fermionic fields both transform in the adjoint representation, a model with SO(N) symmetry in which the scalar and fermion fields both transform as real symmetric-traceless matrices, and a model with SO(N) symmetry in which the scalar field transforms as a real symmetric-traceless matrix, while the fermion transforms in the adjoint representation. These models differ at finite N, but their large-N limits are perturbatively equivalent. The first two models contain a supersymmetric fixed point for all N, which is attractive to all classically-marginal deformations for N sufficiently large. The third model possesses a stable fixed point that, although non-supersymmetric, gives rise to many correlation functions that are identical to those of a supersymmetric fixed point when N is sufficiently large. We also find several non-supersymmetric fixed points at finite and large-N. Planar diagrams dominate the large-N limit of these fixed points, which suggests the possibility of a stringy holographic dual description.

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Critical behavior of Dirac fermions from perturbative renormalization

Cited by 74 publications

References 117 publications

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

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

Universal Prethermal Dynamics in Gross-Neveu-Yukawa Criticality

Emergent supersymmetry at large N

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