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arXiv:2208.00730 · Annals of Physics

Field-theoretic functional renormalization group formalism for non-Fermi liquids and its application to the antiferromagnetic quantum critical metal in two dimensions

Francisco Borges, Anton Borissov, Ashutosh Singh, Andrés Schlief, Sung-Sik Lee

Published Jan 13, 2023• 19 citations
arXivHTMLPDF
DOI
10.1016/j.aop.2023.169221

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This thesis is concerned with recent progress made for the antiferromagnetic quantum critical metal in two space dimensions. Firstly, we develop a field-theoretic functional renormalization group formalism for the low-energy effective field theories for non-Fermi liquids by using renormalizable field theories for metals. The formalism is applied to the antiferromagnetic quantum critical metal in two space dimensions. In the space of coupling functions, we identify the interacting fixed point with a vanishing nesting angle. For theories with non-zero nesting angles, the coupling functions acquire universal momentum dependent profiles controlled by the bare nesting angle before flowing towards a superconducting state in the low-energy limit. The superconducting instability is inevitable because “lukewarm” electrons that are coherent enough to be susceptible to pairing are subject to a universal attractive interaction mediated by the critical spin fluctuations. Despite the superconducting instability being unavoidable, theories with repulsive or weakly attractive four-fermion interaction at a UV scale must flow through a “bottleneck” where there is a slow RG flow due to the proximity to non-Hermitian fixed points. This bottleneck of the RG flow controls the scaling behaviour of the normal state and the “quasi-universal” pathway to superconductivity. Secondly, we show that momentum-dependent quantum corrections dynamically give rise to a curved momentum-spacetimes for quasiparticles. In the antiferromagnetic quantum critical metal, the curved momentum-spacetime geometry arises from a momentum-dependent red shift. With increasing nesting angle, the red shift near the hot spots becomes stronger while the hot region on the Fermi surface with the strong red shift shrinks. This creates the possibility of realizing a momentum-space black hole horizon where electrons are perpetually slowed down as they approach the hot spots. However, the singularity in the momentum-dependent red shift is cut off at finite temperatures above the superconducting transition temperature. Finally, we study a magnetic impurity immersed in the antiferromagnetic quantum critical metal. Critical spin fluctuations represented by bosonic fields compete with the conduction electrons to couple with the impurity spin. In the low-energy limit, the electron-impurity (Kondo) coupling dominates over the boson-impurity coupling. However, the Kondo screening is suppressed by the boson with an increasing severity when the hot spots connected by the antiferromagnetic ordering wavevector are better nested. The origin of this suppression of Kondo screening lies in the ultraviolet/infrared (UV/IR) mixing: bosons that carry large momenta up to the UV cutoff actively suppress the Kondo screening at low energies.
In this thesis we study the scaling properties of unconventional metals that arise at quantum critical points using low-energy effective field theories. Due to high rate of scatterings between electrons and critical fluctuations of the order parameter associated with spontaneous symmetry breaking, Landau’s Fermi liquid theory breaks down at the critical points. The theories that describe these critical points generally flow into strong coupling regimes at low energy in two space dimensions. Here we develop and utilize renormalization group methods that are suitable for the interacting non-Fermi liquids. We focus on the critical points arising at excitonic, and commensurate spin and charge density wave transitions. By controlled analyses we find stable non-Fermi liquid and marginal Fermi liquid states, and extract the scaling behaviour. The field theories for the non-Fermi liquids are characterized by symmetry groups, local curvature of the Fermi surface, the dispersion of the order parameter fluctuations, and dimensions of space and Fermi surface.