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Register a new userEmergence of a control parameter for the antiferromagnetic quantum critical metal
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We study the antiferromagnetic quantum critical metal in $3-epsilon$ space dimensions by extending the earlier one-loop analysis [Sur and Lee, Phys. Rev. B 91, 125136 (2015)] to higher-loop orders. We show that the $epsilon$-expansion is not organized by the standard loop expansion, and a two-loop graph becomes as important as one-loop graphs due to an infrared singularity caused by an emergent quasilocality. This qualitatively changes the nature of the infrared (IR) fixed point, and the $epsilon$-expansion is controlled only after the two-loop effect is taken into account. Furthermore, we show that a ratio between velocities emerges as a small parameter, which suppresses a large class of diagrams. We show that the critical exponents do not receive corrections beyond the linear order in $epsilon$ in the limit that the ratio of velocities vanishes. The $epsilon$-expansion gives critical exponents which are consistent with the exact solution obtained in $0 < epsilon leq 1$.
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Unconventional metallic states which do not support well defined single-particle excitations can arise near quantum phase transitions as strong quantum fluctuations of incipient order parameters prevent electrons from forming coherent quasiparticles. Although antiferromagnetic phase transitions occur commonly in correlated metals, understanding the nature of the strange metal realized at the critical point in layered systems has been hampered by a lack of reliable theoretical methods that take into account strong quantum fluctuations. We present a non-perturbative solution to the low-energy theory for the antiferromagnetic quantum critical metal in two spatial dimensions. Being a strongly coupled theory, it can still be solved reliably in the low-energy limit as quantum fluctuations are organized by a new control parameter that emerges dynamically. We predict the exact critical exponents that govern the universal scaling of physical observables at low temperatures.
We compute the scrambling rate at the antiferromagnetic (AFM) quantum critical point, using the fixed point theory of Phys. Rev. X $boldsymbol{7}$, 021010 (2017). At this strongly coupled fixed point, there is an emergent control parameter $w ll 1$ 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 $lambda_L^{(B)} sim mathcal O(sqrt{w}) ,k_B T/hbar$ is significantly larger than the fermion one $lambda_L^{(F)} sim mathcal O(w^2) ,k_B T/hbar$, where $T$ 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 $lambda_L=2pi k_B T/hbar$. 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.
We present numerically exact results from sign-problem free quantum Monte Carlo simulations for a spin-fermion 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 ($Tge E_F/200$), we find substantial deviations from the $z=2$ Hertz-Millis behavior, but no evidence for the predicted $z=1$ criticality.
Quantum criticality is a central concept in condensed matter physics, but the direct observation of quantum critical fluctuations has remained elusive. Here we present an x-ray diffraction study of the charge density wave (CDW) in 2H-NbSe2 at high pressure and low temperature, where we observe a broad regime of order parameter fluctuations that are controlled by proximity to a quantum critical point. X-rays can track the CDW despite the fact that the quantum critical regime is shrouded inside a superconducting phase, and, in contrast to transport probes, allow direct measurement of the critical fluctuations of the charge order. Concurrent measurements of the crystal lattice point to a critical transition that is continuous in nature. Our results confirm the longstanding expectations of enhanced quantum fluctuations in low dimensional systems, and may help to constrain theories of the quantum critical Fermi surface.
One of the most exciting discoveries in strongly correlated systems has been the existence of a superconducting dome on heavy fermions close to the quantum critical point where antiferromagnetic order disappears. It is hard even for the most skeptical not to admit that the excitations which bind the electrons in the Cooper pairs have a magnetic origin. As a system moves away from an antiferromagnetic quantum critical point, (AFQCP) the correlation length of the fluctuations decreases and the system goes into a local quantum critical regime. The attractive interaction mediated by the non-local part of these excitations vanishes and this allows to obtain an upper bound to the superconducting dome around an AFQCP.
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