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arXiv:2604.24274

Umklapp correction to Landau damping and conditions for non-trivial modifications to quantum critical transport

Vibhu Mishra

Published Apr 27, 2026• 0 citations
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Abstract

We compute the particle--hole bubble for an Ising-nematic metal when the critical Fermi surface approaches the Brillouin zone boundary for $d=2$ dimensions. We find two qualitatively distinct contributions: i)~the standard antipodal piece, which gives $Π_{\rm{ATP}}(\mathbf{q}, iΩ)\proptoΩ/q$ and ii)~an additional umklapp piece from electrons near the zone boundary, which gives $Π_{\rm{U}}(\mathbf{q}, iΩ)\propto Ω^α$ at the minimum umklapp momentum $q\approx Δ_q$ with $α= 2/3 $ or $1/2$ depending on the temperature $T$. At high $T$ when $α= 1/2$, the minimum $T$ for the activation of linear/quasi-linear in $T$ resistivity, which is expected to be $T_U \propto Δ_q^3$ from $z=3$ criticality, could potentially get reduced to $T_U \propto Δ_q^4$ due to the $\sqrtΩ$ term and discuss why we find only one hyper-specific scenario where this possibility might be realized. For $d=3$ the umklapp contribution gives $Π_{\rm{U}}\sim Ω$ irrespective of $T$ therefore $T_U$ is not modified in this case.

DOI
10.48550/arxiv.2604.24274

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The instability of a Fermi surface against Ising nematic order destroys the quasiparticle character of the low-energy degrees of freedom. Therefore, observables exhibit deviations from Fermi liquid behavior which gives rise to the term Ising nematic quantum critical metal. To obtain a theoretical description we use a finite-temperature version of Eliashberg theory which allows to treat the strong coupling between quantum and thermal fluctuations in the absence of well-defined quasiparticles. Here, we use this self-consistent, diagrammatic approach to compute, in particular, the nematic susceptibility and the non-Fermi liquid correlations. Upon decreasing the temperature, the susceptibility crosses over from a (Tlog⁡T)−1(T \log T)^{-1}(TlogT)−1 to T−2/3T^{-2/3}T−2/3 behavior, which is induced by the absence of quasiparticles and restores the Ising nematic critical scaling. Correspondingly, the fermions obey a simple ω/Tω/Tω/T scaling law at low enough temperatures. However, this regime is characterized by strong IR-UV mixing since the proportionality factors exhibit a dependence on the spectral width of the non-quasiparticle excitations and on the underlying lattice. Tuning the parameters of the model, therefore, gives rise to several scenarios for the breakdown of the scaling theory. We discuss them within the Eliashberg approach and estimate the related crossover scales. We also show that the leading order vertex corrections do not change the scaling with temperature or coupling constants.
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