Exact Critical Exponents for the Antiferromagnetic Quantum Critical Metal in Two Dimensions

Abstract

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 lowenergy 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.

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

“…However, we neither observe a dynamical critical exponent z = 1 nor a momentum-anisotropy in the propagation of magnetic modes for our model parameters. This leaves us with the conclusion that, within the resolution of our DQMC simulations for systems of linear size L ≤ 14 and temperatures T ≥ E F 200, we cannot numerically observe the new fixed point discovered by Schlief et al [26] in our O(3) spin-fermion model.…”

“…We start off by discussing a potential superconducting transition. In an almost locally nested system antiferromagnetic fluctuations will only slightly enhance T c [5,18,26]. As indicated in Eq.…”

“…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.…”

“…Finally, we search for the regime described by Schlief et al [26], which is characterized by a z = 1 dynamical scaling and strongly spatially anisotropic SDW order parameter correlations. To that end, we conduct an ultra-low temperature (down to T ∼ E F 200) DQMC study for a Fermi surface tuned close to local nesting at the hot spots -a scenario that is expected to bring us closer to the z = 1 fixed point [26,27]. Indeed, we observe strong deviations in the Matsubara frequency and momentum dependence of the SDW propagator from the Hertz-Millis form.…”

The unreasonable effectiveness of Eliashberg theory for pairing of non-Fermi liquids

“…Quite interestingly, in some of the examples where Eliashberg theory appears to work well without any formal justification [31], it is unclear what is responsible for this agreement. This is not to say, however, that all non-Fermi liquids are well-described by Eliashberg theory; for instance, a recent work revealed a strongly coupled fixed point of a nearly antiferromagnetic metal, with a very different structure [79], which is controlled by an emergent small parameter. The search for such new non-perturbative fixed points, as well as other controlled limits of correlated electron systems, is bound to provide new insights into the complexity of the growing class of correlated quantum materials.…”