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arXiv:2302.04172 · Physical review. B./Physical review. B

Non-Fermi liquid behavior at flat hot spots from quantum critical fluctuations at the onset of charge- or spin-density wave order

Lukas Debbeler, Walter Metzner

Published Apr 26, 2023• 5 citations
arXivHTMLPDF

Abstract

We analyze quantum fluctuation effects at the onset of charge- or spin-density wave order with a $2{k}_{F}$ wave vector $\mathbf{Q}$ in two-dimensional metals, for the special case where $\mathbf{Q}$ connects a pair of hot spots situated at high symmetry points of the Fermi surface with a vanishing Fermi surface curvature. We compute the order parameter susceptibility and the fermion self-energy in one-loop approximation. The susceptibility has a pronounced peak at $\mathbf{Q}$, and the self-energy displays non-Fermi liquid behavior at the hot spots, with a linear frequency dependence of its imaginary part. The real part of the one-loop self-energy exhibits logarithmic divergencies with universal prefactors as a function of both frequency and momentum, which may be interpreted as perturbative signatures of power laws with universal anomalous dimensions. As a result, one obtains a non-Fermi liquid metal with a vanishing quasiparticle weight at the hot spots, and a renormalized dispersion relation with anomalous algebraic momentum dependencies near the hot spots.

DOI
10.1103/physrevb.107.165152

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We analyze quantum fluctuation effects at the onset of charge or spin density wave order in two-dimensional metals with an incommensurate 2kF2{k}_{F}2kF​ wave vector connecting a single pair of hot spots on the Fermi surface. We compute the momentum and frequency dependence of the fermion self-energy near the hot spots to leading order in a fluctuation expansion (one loop). Non-Fermi liquid behavior with anomalous frequency scaling and a vanishing quasiparticle weight is obtained. The momentum dependence yields a divergent renormalization of the Fermi velocity and a flattening of the Fermi surface near the hot spots. Going beyond the leading-order calculation, we find that the one-loop result is not self-consistent. We show that any momentum-independent self-energy with a non-Fermi liquid frequency exponent wipes out the peak of the polarization function at the 2kF2{k}_{F}2kF​ wave vector, and thus destroys the mechanism favoring 2kF2{k}_{F}2kF​ density waves over those with generic wave vectors. However, a 2kF2{k}_{F}2kF​ density wave quantum critical point might survive in presence of a sufficiently flat renormalized Fermi surface.
We analyze quantum fluctuation effects at the onset of incommensurate 2 k F charge- or spin-density-wave order in two-dimensional metals for a model in which the ordering wave vector Q connects a single pair of hot spots on the Fermi surface with a vanishing Fermi surface curvature. The tangential momentum dependence of the bare dispersion near the hot spots is proportional to | k t | α with α > 2 . We first compute the order parameter susceptibility and the fermion self-energy in a random phase approximation (RPA). Logarithmic divergences are subsequently treated by a renormalization-group analysis. The coupling between the order parameter fluctuations and the fermions vanishes logarithmically in the low-energy limit. As a consequence, the logarithmic divergences found in the RPA do not sum up to anomalous power laws. Instead, only logarithmic corrections to Fermi liquid behavior are obtained. In particular, the quasiparticle weight and the Fermi velocity vanish logarithmically at the hot spots. Published by the American Physical Society 2024
We analyze quantum fluctuation effects at the onset of charge or spin-density wave order in two-dimensional metals with an incommensurate nesting (2kF2{k}_{F}2kF​) wave vector connecting two pairs of hot spots on the Fermi surface. We first compute the momentum and frequency dependence of the fermion self-energy near the hot spots to leading order in a perturbation expansion (one loop). Non-Fermi liquid behavior with a linear (in energy) quasiparticle decay rate and a logarithmically vanishing quasiparticle weight is obtained. The momentum dependence of the self-energy entails only finite renormalizations of the Fermi velocity and the Fermi-surface curvature at the hot spots. The perturbative one-loop result is not self-consistent and casts doubt on the stability of the 2kF2{k}_{F}2kF​ quantum critical point. We construct a self-consistent solution of the one-loop equations with self-energy feedback, where the quantum critical point is stabilized rather than being destroyed by fluctuations, while the non-Fermi liquid behavior as found in the perturbative one-loop calculation is confirmed.
We analyze the influence of quantum critical fluctuations on single-particle excitations at the onset of incommensurate 2kF2{k}_{F}2kF​ charge- or spin-density wave order in two-dimensional metals. The case of a single pair of hot spots at high symmetry positions on the Fermi surface needs to be distinguished from the case of two hot spot pairs. We compute the fluctuation propagator and the electronic self-energy perturbatively in leading order. The energy dependence of the single-particle decay rate at the hot spots obeys non-Fermi-liquid power laws, with an exponent 2/3 in the case of a single hot spot pair, and exponent one for two hot spot pairs. The prefactors of the linear behavior obtained in the latter case are not particle-hole symmetric.
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 $(3\ensuremath{-}\ensuremath{\epsilon})$-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 wave vector 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 $\ensuremath{\epsilon}$, 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 antiscreens the coupling at the SDW critical point whereas it screens at the CDW critical point.
We consider the emergence of a non-Fermi liquid fixed point in two-dimensional metals at the onset of a quantum phase transition from a Fermi liquid state to an incommensurate charge density wave (CDW) ordered phase. The momentum of the CDW boson is centred at the wavevector Q, which connects a single pair of antipodal points on the Fermi surface with antiparallel tangent vectors. We employ the dimensional regularization technique in which the co-dimension of the Fermi surface is extended to a generic value, while keeping the dimension of Fermi surface itself fixed at one. Although the system is strongly coupled at dimension d=2, the interactions become marginal at the upper critical dimension d=dc, whose value is found to be 5/2. Using a controlled perturbative expansion in the parameter ϵ=dc−d, we compute the critical exponents of the stable infrared fixed point characterizing the quantum critical point. The scalings of the original theory are determined by setting ϵ=1/2, where the fermion self-energy is seen to scale with the frequency with a fractional power law of 2/3, which is the telltale signature of a typical non-Fermi liquid phase.