Emergence of a control parameter for the antiferromagnetic quantum critical metal

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

doi:10.1103/physrevb.95.245109

Cited by 29 publications

(44 citation statements)

References 61 publications

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“…Motivated by the recent prediction of a novel z = 1 fixed point [26][27][28] by Sung-Sik Lee and collaborators, we consid-ered a variant of the model where the hot spots are (nearly) locally nested. In this case, the superconducting T c is strongly suppressed below the lowest temperature available in our study, T ≈ E F 200.…”

Section: Discussionmentioning

confidence: 99%

“…Many intensive analytical efforts have been made to get a handle on strong interactions and gain control over calculations. These include various 1 N -expansions [5,15,22] and extensions of the problem to fractional dimensions [27,51]. One of the more striking developments has been a recent, self-consistent and non-perturbative study which has been put forward by Schlief et al [26].…”

Section: Theoretical Backgroundmentioning

confidence: 99%

“…An audacious line of research [26][27][28] carried out by Sung-Sik Lee and collaborators, however, has recently made notable progress in identifying a route to a controlled expansion in an emergent control parameter to compute the properties of a strongly coupled fixed point at the O(3) antiferromagnetic QCP in an exact manner. One concrete prediction of this non-perturbative analysis is a low temperature regime exhibiting a dynamical scaling exponent z = 1 [26][27][28]. At this fixed point, the tendency towards superconductivity is strongly suppressed.…”

Section: Introductionmentioning

confidence: 99%

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Hierarchy of energy scales in an O(3) symmetric antiferromagnetic quantum critical metal: A Monte Carlo study

Bauer

Schattner

Berg

2020

Phys. Rev. Research

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We present numerically exact results from sign-problem free quantum Monte Carlo simulations for a spinfermion model near an O(3) symmetric antiferromagnetic (AFM) quantum critical point. We find a hierarchy of energy scales that emerges near the quantum critical point. At high energy scales, there is a broad regime characterized by Landau-damped order parameter dynamics with dynamical critical exponent z = 2, while the fermionic excitations remain coherent. The quantum critical magnetic fluctuations are well described by Hertz-Millis theory, except for a T −2 divergence of the static AFM susceptibility. This regime persists down to a lower energy scale, where the fermions become overdamped and concomitantly, a transition into a d−wave superconducting state occurs. These findings resemble earlier results for a spin-fermion model with easy-plane AFM fluctuations of an O(2) SDW order parameter, despite noticeable differences in the perturbative structure of the two theories. In the O(3) case, perturbative corrections to the spin-fermion vertex are expected to dominate at an additional energy scale, below which the z = 2 behavior breaks down, leading to a novel z = 1 fixed point with emergent local nesting at the hot spots [Schlief et al., PRX 7, 021010 (2017)]. Motivated by this prediction, we also consider a variant of the model where the hot spots are nearly locally nested. Within the available temperature range in our study (T ≥ E F 200), we find substantial deviations from the z = 2 Hertz-Millis behavior, but no evidence for the predicted z = 1 criticality. arXiv:2001.00586v3 [cond-mat.str-el]

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Section: Discussionmentioning

confidence: 99%

Section: Theoretical Backgroundmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Hierarchy of energy scales in an O(3) symmetric antiferromagnetic quantum critical metal: A Monte Carlo study

Bauer

Schattner

Berg

2020

Phys. Rev. Research

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“…There are several examples of CFTs with fermionic degrees of freedom that can be studied in ϵ-expansion and to which the method we describe here is applicable, see for instance the recent works [18][19][20][21][22][23][24][25][26][27][28][29][30] and references therein. In our companion paper [31], we focus on 3d QED and use the NLO eigenvalues obtained here to estimate the scaling dimensions of four-fermion operators in d ¼ 3.…”

Section: Introductionmentioning

confidence: 99%

Operator mixing in the ε -expansion: Scheme and evanescent-operator independence

Pietro

Stamou

2018

Phys. Rev. D

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We consider theories with fermionic degrees of freedom that have a fixed point of Wilson-Fisher type in noninteger dimension d ¼ 4 − 2ϵ. Due to the presence of evanescent operators, i.e., operators that vanish in integer dimensions, these theories contain families of infinitely many operators that can mix with each other under renormalization. We clarify the dependence of the corresponding anomalous-dimension matrix on the choice of renormalization scheme beyond leading order in ϵ-expansion. In standard choices of scheme, we find that eigenvalues at the fixed point cannot be extracted from a finite-dimensional block. We illustrate in examples a truncation approach to compute the eigenvalues. These are observable scaling dimensions, and, indeed, we find that the dependence on the choice of scheme cancels. As an application, we obtain the IR scaling dimension of four-fermion operators in QED in d ¼ 4 − 2ϵ at order Oðϵ 2 Þ.

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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%

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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Emergence of a control parameter for the antiferromagnetic quantum critical metal

Cited by 29 publications

References 61 publications

Hierarchy of energy scales in an O(3) symmetric antiferromagnetic quantum critical metal: A Monte Carlo study

Hierarchy of energy scales in an O(3) symmetric antiferromagnetic quantum critical metal: A Monte Carlo study

Operator mixing in the ε -expansion: Scheme and evanescent-operator independence

Many-body chaos in the antiferromagnetic quantum critical metal

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