Universality in antiferromagnetic strange metals

Abstract

We propose a theory of metals at the spin-density wave quantum critical point in spatial dimension $d=2$. We provide a first estimate of the full set of critical exponents (dynamical exponent $z=2.13$, correlation length $\nu =1.02$, spin susceptibility $\gamma =0.96$, electronic non-Fermi liquid ${\eta }_{\tau }^f=0.53$, spin-wave Landau damping ${\eta }_{\tau }^b=1.06$), which determine the universal power-laws in thermodynamics and response functions in the quantum-critical regime relevant for experiments in heavy-fermion systems and iron pnictides. We present approximate numerical and analytical solutions of Polchinski-Wetterich type flow equations with soft frequency regulators for an effective action of electrons coupled to spin-wave bosons. Performing the renormalization group in frequency -instead of momentum- space allows to track changes of the Fermi surface shape and to capture Landau damping during the flow. The technique is easily generalizable from models retaining only patches of the Fermi surface to full, compact Fermi surfaces.

46 pages, 13 figures, typos fixed; as accepted to Physical Review B

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• Holographic quantum matter
• Recent Developments in Non-Fermi Liquid Theory
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• Exact critical exponents for the antiferromagnetic quantum critical metal in two dimensions
• Quantum critical properties of a metallic spin density wave transition
• Quantum criticality with a twist - interplay of correlations and Kohn anomalies in three dimensions
• Anisotropic Non-Fermi Liquids
• Emergence of a control parameter for the antiferromagnetic quantum critical metal
• Pairing in quantum-critical systems: $T_c$, $\Delta$, and their ratio
• Spin density wave order, topological order, and Fermi surface reconstruction
• Field-theoretic functional renormalization group formalism for non-Fermi liquids and its application to the antiferromagnetic quantum critical metal in two dimensions
• Fluctuation effects at the onset of $2{\mathbf{k}}_{\mathbf{F}}$ density wave order with one pair of hot spots in two-dimensional metals
• Noncommutativity between the low-energy limit and integer dimension limits in the $\mathbf{\epsilon }$-expansion: a case study of the antiferromagnetic quantum critical metal
• Robustness of quantum critical pairing against disorder
• Incommensurate $2k_F$ density wave quantum criticality in two dimensional metals
• Space of non-Fermi liquids
• Fluctuation effects at the onset of $2{\mathbf{k}}_{\mathbf{F}}$ density wave order with two pairs of hot spots in two-dimensional metals
• Non-Fermi liquid fixed points and anomalous Landau damping in a quantum critical metal
• Many-body chaos in the antiferromagnetic quantum critical metal
• Interaction-enhanced nesting in Spin-Fermion and Fermi-Hubbard models
• Ladder-like optical conductivity in the spin-fermion model
• Emergence of curved momentum-spacetime and its effect on the cyclotron motion in the antiferromagnetic quantum critical metal
• Dynamical kinetic energy quenching in the antiferromagnetic quantum critical metals