Anisotropic Non-Fermi Liquids

Abstract

We study non-Fermi liquid states that arise at the quantum critical points associated with the spin density wave (SDW) and charge density wave (CDW) transitions in metals with twofold rotational symmetry. We use the dimensional regularization scheme, where a one-dimensional Fermi surface is embedded in $3-\epsilon$ dimensional momentum space. In three dimensions, quasilocal marginal Fermi liquids arise both at the SDW and CDW critical points : the speed of the collective mode along the ordering wavevector is logarithmically renormalized to zero compared to that of Fermi velocity. Below three dimensions, however, the SDW and CDW critical points exhibit drastically different behaviors. At the SDW critical point, a stable anisotropic non-Fermi liquid state is realized for small $\epsilon$, where not only time but also different spatial coordinates develop distinct anomalous dimensions. The non-Fermi liquid exhibits an emergent algebraic nesting as the patches of Fermi surface are deformed into a universal power-law shape near the hot spots. Due to the anisotropic scaling, the energy of incoherent spin fluctuations disperse with different power laws in different momentum directions. At the CDW critical point, on the other hand, the perturbative expansion breaks down immediately below three dimensions as the interaction renormalizes the speed of charge fluctuations to zero within a finite renormalization group scale through a two-loop effect. The difference originates from the fact that the vertex correction anti-screens the coupling at the SDW critical point whereas it screens at the CDW critical point.

27 pages, 15 figures; v2) References & clarification added

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• Recent Developments in Non-Fermi Liquid Theory
• Exact critical exponents for the antiferromagnetic quantum critical metal in two dimensions
• Itinerant Quantum Critical Point with Fermion Pockets and Hot Spots
• Revealing Fermionic Quantum Criticality from New Monte Carlo Techniques
• Itinerant quantum critical point with frustration and non-Fermi-liquid
• Fate of superconductivity in three-dimensional disordered Luttinger semimetals
• Emergent Anisotropic Non-Fermi Liquid at a Topological Phase Transition in Three Dimensions
• UV/IR Mixing In Non-Fermi Liquids: Higher-Loop Corrections In Different Energy Ranges
• Unifying Interacting Nodal Semimetals: A New Route to Strong Coupling
• Emergence of a control parameter for the antiferromagnetic quantum critical metal
• Metallic and Deconfined Quantum Criticality in Dirac Systems
• Scaling behaviour and superconducting instability in anisotropic non-Fermi liquids
• Field-theoretic functional renormalization group formalism for non-Fermi liquids and its application to the antiferromagnetic quantum critical metal in two dimensions
• Operator mixing in $\mathbf{\epsilon }$-expansion: scheme and evanescent (in)dependence
• EMUS-QMC: Elective Momentum Ultra-Size Quantum Monte Carlo Method
• Search for plasmons in isotropic Luttinger semimetals
• Quantum Interference of Hydrodynamic Modes in a Dirty Marginal Fermi Liquid
• Anomalous thermodynamic properties of quantum critical superconductors
• Noncommutativity between the low-energy limit and integer dimension limits in the $\mathbf{\epsilon }$-expansion: a case study of the antiferromagnetic quantum critical metal
• Long-range Coulomb Interaction effects on Topological Phase Transitions between Semi-metals and Insulators
• Quantum Criticalities with Infinite Anisotropy in Topological Phase Transitions between Dirac and Weyl Semi-metals
• Critical properties of metallic and deconfined quantum phase transitions in Dirac systems
• Space of non-Fermi liquids
• Fermi liquids beyond the forward scattering limit: the role of non-forward scatterings for scale invariance and instabilities
• The Kondo-lattice state in the presence of Van Hove singularities: a next-leading order scaling description
• Axionic quantum criticality of generalized Weyl semimetals
• Anomalous quasiparticle lifetime in geometric quantum critical metals
• Dynamical kinetic energy quenching in the antiferromagnetic quantum critical metals