Noncommutativity between the low-energy limit and integer dimension limits in the 
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 expansion: A case study of the antiferromagnetic quantum critical metal

Schlief, Andrés; Lunts, Peter; Lee, Sung-Sik

doi:10.1103/physrevb.98.075140

Cited by 13 publications

(8 citation statements)

References 72 publications

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“…It plays a vital role in the understanding of anomalous transport, strange metal, and non–Fermi-liquid behaviors (9–13) in heavy-fermion materials (14, 15), Cu- and Fe-based high-temperature superconductors (16–18) as well as the recently discovered pressure-driven quantum critical point (QCP) between magnetic order and superconductivity in transition-metal monopnictides, CrAs (19), MnP (20), CrAs1−xnormalPx (21), and other Cr/Mn-3d electron systems (22). However, despite extensive efforts in recent decades (1–9, 23–30), itinerant quantum criticality is still among the most challenging subjects in condensed matter physics, due to its nonperturbative nature, and many important questions and puzzles remain open.…”

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confidence: 99%

Itinerant quantum critical point with fermion pockets and hotspots

Liu

Pan

et al. 2019

Proc. Natl. Acad. Sci. U.S.A.

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Metallic quantum criticality is among the central themes in the understanding of correlated electronic systems, and converging results between analytical and numerical approaches are still under review. In this work, we develop a state-of-the-art large-scale quantum Monte Carlo simulation technique and systematically investigate the itinerant quantum critical point on a 2D square lattice with antiferromagnetic spin fluctuations at wavevector Q=(π,π)—a problem that resembles the Fermi surface setup and low-energy antiferromagnetic fluctuations in high-Tc cuprates and other critical metals, which might be relevant to their non–Fermi-liquid behaviors. System sizes of 60×60×320 (L×L×Lτ) are comfortably accessed, and the quantum critical scaling behaviors are revealed with unprecedented high precision. We found that the antiferromagnetic spin fluctuations introduce effective interactions among fermions and the fermions in return render the bare bosonic critical point into a different universality, different from both the bare Ising universality class and the Hertz–Mills–Moriya RPA prediction. At the quantum critical point, a finite anomalous dimension η∼0.125 is observed in the bosonic propagator, and fermions at hotspots evolve into a non-Fermi liquid. In the antiferromagnetically ordered metallic phase, fermion pockets are observed as the energy gap opens up at the hotspots. These results bridge the recent theoretical and numerical developments in metallic quantum criticality and can serve as the stepping stone toward final understanding of the 2D correlated fermions interacting with gapless critical excitations.

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confidence: 99%

Itinerant quantum critical point with fermion pockets and hotspots

Liu

Pan

et al. 2019

Proc. Natl. Acad. Sci. U.S.A.

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“…Further analysis, and exploration at higher loop order is required to make concrete conclusions. Finally, it would be interesting to study the crossover behavior from perturbative to integer d L -d Q systems, similar to recent work on quantum critical metals [76]. There it was found that low energy and integer dimension limits do not commute.…”

Section: Discussionmentioning

confidence: 58%

Fermionic criticality of anisotropic nodal point semimetals away from the upper critical dimension: exact $1/N_f$ exponents

Uryszek,

Krüger,

Christou

2020

Preprint

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We consider the fermionic quantum criticality of anisotropic nodal point semimetals in d = dL + dQ spatial dimensions that disperse linearly in dL dimensions, and quadratically in the remaining dQ dimensions. When subject to strong interactions, these systems are susceptible to semimetalinsulator transitions concurrent with spontaneous symmetry breaking. Such quantum critical points are described by effective field theories of anisotropic nodal fermions coupled to dynamical order parameter fields. We analyze the universal scaling in the physically relevant spatial dimensions, generalizing to a large number N f of fermion flavors for analytic control. Landau damping by gapless fermionic excitations gives rise to non-analytic self-energy corrections to the bosonic order-parameter propagator that dominate the long-wavelength behavior. We show that perturbative momentum shell RG leads to non-universal, cutoff dependent results, as it does not correctly account for this non-analytic structure. In turn, using a completely general soft cutoff formulation, we demonstrate that the correct IR scaling of the dressed bosonic propagator can be deduced by enforcing that results are independent of the cutoff scheme. Using this soft cutoff approach, we compute the exact critical exponents for anisotropic semi-Dirac fermions (dL = 1, dQ = 1) to leading order in 1/N f , and to all loop orders. Applying the same method to relativistic Dirac fermions, we reproduce the critical exponents obtained by other methods, such as conformal bootstrap. Unlike in the relativistic case, where the UV-IR connection is re-established at the upper critical dimension, non-analytic IR contributions persist near the upper critical line 2dL + dQ = 4 of anisotropic nodal fermions. We present -expansions in both the number of linear and quadratic dimensions. The corrections to critical exponents are non-analytic in , with a functional form that depends on the starting point on the upper critical line.

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“…The spin-fermion model [33][34][35][36][37][38][39][40][41][42][43][44][45] describes a system of two-dimensional electrons interacting with a collective spin excitation at a finite ordering wavevector. This interaction is strongest at certain "hot spots" on the Fermi surface that are connected by the ordering wavevector.…”

Section: Modelmentioning

confidence: 99%

“…In this work we study many-body quantum chaos at the antiferromagnetic (AFM) quantum critical point (QCP) of a two-dimensional metal, believed to exist in a wide range of layered compounds [30][31][32]. It is described by the spin-fermion model [33][34][35][36][37][38][39][40][41][42][43][44][45], in which the fluctuations of the AFM collective bosonic mode scatter electrons between pairs of "hot spots". The stable low energy fixed point of this model was found in Ref.…”

Section: Introductionmentioning

confidence: 99%

Many-body chaos in the antiferromagnetic quantum critical metal

Lunts

Patel

2019

Phys. Rev. B

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We compute the scrambling rate at the antiferromagnetic (AFM) quantum critical point, using the fixed point theory of Phys. Rev. X 7, 021010 (2017). At this strongly coupled fixed point, there is an emergent control parameter w 1 that is a ratio of natural parameters of the theory. The strong coupling is unequally felt by the two degrees of freedom: the bosonic AFM collective mode is heavily dressed by interactions with the electrons, while the electron is only marginally renormalized. We find that the scrambling rates act as a measure of the "degree of integrability" of each sector of the theory: the Lyapunov exponent for the boson λwhere T is the temperature. Although the interaction strength in the theory is of order unity, the larger Lyapunov exponent is still parametrically smaller than the universal upper bound of λL = 2πkBT / . We also compute the spatial spread of chaos by the boson operator, whose low-energy propagator is highly non-local. We find that this non-locality leads to a scrambled region that grows exponentially fast, giving an infinite "butterfly velocity" of the chaos front, a result that has also been found in lattice models with long-range interactions.

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Noncommutativity between the low-energy limit and integer dimension limits in the ε expansion: A case study of the antiferromagnetic quantum critical metal

Cited by 13 publications

References 72 publications

Itinerant quantum critical point with fermion pockets and hotspots

Itinerant quantum critical point with fermion pockets and hotspots

Fermionic criticality of anisotropic nodal point semimetals away from the upper critical dimension: exact $1/N_f$ exponents

Many-body chaos in the antiferromagnetic quantum critical metal

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