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arXiv:2408.06116 · Physical review. B./Physical review. B

Non-Fermi-liquid scaling of the quasiparticle lifetime at a density-wave quantum critical point

Iran Seydi, Saeed H. Abedinpour, Reza Asgari, B. Tanatar

Published Oct 29, 2026• 0 citations
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Abstract

We analytically study the inelastic lifetime of quasiparticles due to particle-particle interactions in a three-dimensional Fermi liquid approaching a density-wave instability. Using the G$_0$W approximation, we find that the softening of the dielectric function significantly enhances the quasiparticle decay rate near the instability. While the zero-temperature quasiparticle lifetime at the Fermi surface generally follows a $|\varepsilon_k-\varepsilon_{\rm F}|^{-α}$ divergence with $α=2$, we observe $α=0.5$ at the instability point and $α=1$ within the density-wave phase. Moreover, we demonstrate that the renormalization constant $Z$ is substantially suppressed as the instability is approached, enhancing the effective mass. We extend our analysis to ultra-cold Rydberg-dressed Fermi liquids, where the soft-core interactions promote density-wave instability, and find that our numerical G$_0$W results are in excellent agreement with our analytic predictions for quasiparticle lifetime, renormalization constant, and effective mass.

DOI
10.1103/vbyz-6gtp

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We analytically study the inelastic lifetime of quasiparticles due to particle-particle interactions in a three-dimensional Fermi liquid approaching a density-wave instability. Using the G0_00​W approximation, we find that the softening of the dielectric function significantly enhances the quasiparticle decay rate near the instability. While the zero-temperature quasiparticle lifetime at the Fermi surface generally follows a ∣εk−εF∣−α|\varepsilon_k-\varepsilon_{\rm F}|^{-α}∣εk​−εF​∣−α divergence with α=2α=2α=2, we observe α=0.5α=0.5α=0.5 at the instability point and α=1α=1α=1 within the density-wave phase. Moreover, we demonstrate that the renormalization constant ZZZ is substantially suppressed as the instability is approached, enhancing the effective mass. We extend our analysis to ultra-cold Rydberg-dressed Fermi liquids, where the soft-core interactions promote density-wave instability, and find that our numerical G0_00​W results are in excellent agreement with our analytic predictions for quasiparticle lifetime, renormalization constant, and effective mass.
We study the quantum critical behavior in an isotropic Fermi liquid in the vicinity of a zero-temperature density-wave transition at a finite wave vector qc{q}_{c}qc​. We show that, near the transition, the Landau damping of the soft bosonic mode yields a crossover in the fermionic self-energy from $\ensuremath{\Sigma}(k,\ensuremath{\omega})\ensuremath{\approx}\ensuremath{\Sigma}(k)$ to $\ensuremath{\Sigma}(k,\ensuremath{\omega})\ensuremath{\approx}\ensuremath{\Sigma}(\ensuremath{\omega})$, where kkk and $\ensuremath{\omega}$ are momentum and frequency. Because of this self-generated locality, the fermionic effective mass diverges right at the quantum critical point, not before; i.e., the Fermi liquid survives up to the critical point.
We analyze the quasiparticle interaction function (the fully dressed and antisymmetrized interaction between fermions) for a two-dimensional Fermi liquid at zero temperature close to a q=0 charge quantum critical point (QCP) in the $s\text{\ensuremath{-}}\mathrm{wave}$ channel (the one leading to phase separation). By the Ward identities, this vertex function must be related to quasiparticle residue ZZZ, which can be obtained independently from the fermionic self-energy. We show that to satisfy these Ward identities, one needs to go beyond the standard diagrammatic formulation of Fermi-liquid theory and include a series of additional contributions to the vertex function. These contributions are not present in a conventional Fermi liquid, but do emerge near a QCP, where the effective 4-fermion interaction is mediated by a soft dynamical boson. We demonstrate explicitly that including these terms restores the Ward identity. Our analysis is built on previous studies of the vertex function near an antiferromag netic QCP [Phys. Rev. B 89, 045108 (2014)] and a ddd-wave charge-nematic QCP [Phys. Rev. B 81, 045110 (2010)]. We show th at for $s\text{\ensuremath{-}}\mathrm{wave}$ charge QCP the analysis is more straightforward and allows one to obtain the full quasiparticle interaction function (the Landau function) near a QCP. We show that all partial components of this function (Landau parameters) diverge near a QCP, in the same way as the effective mass m∗{m}^{*}m∗, except for the sss-wave charge component, which approaches $\ensuremath{-}1$. Consequently, the susceptibilities in all channels, except for the critical one, remain finite at a QCP, as they should.
In interacting quantum systems, the single-particle Green's function is expected to decay in time due to the interaction induced decoherence of quasiparticles. In the limit of weak interaction strengths (ΔΔΔ), a naive application of Fermi's Golden Rule (FGR) predicts an O(Δ2)\mathcal{O}(Δ^{2})O(Δ2) quasiparticle decay rate. However, for 1d fermions on the lattice at T>0T>0T>0, this calculation gives a divergent result and the scaling of the quasiparticle lifetime with interaction strength remains an open question. In this work we propose a solution to this question: combining numerical simulations using the recently introduced dissipation-assisted operator evolution (DAOE) method, with non-perturbative diagrammatic re-summations, we predict a logarithmic enhancement of the quasiparticle decay rate τ−1∼Δ2log⁡Δ−2τ^{-1} \sim Δ^{2} \log Δ^{-2}τ−1∼Δ2logΔ−2. We argue that this effect is present in a wide variety of well-known weakly interacting quantum fermionic and bosonic systems, and even in some classical systems, provided the non-interacting limit has quasiparticles with a generic dispersion.
Interactions in Fermi systems can generate a Pomeranchuk instability leading to orientational symmetry breaking, that is, nematic order. In a metallic system close to such an instability the Fermi surface is easily deformed by anisotropic perturbations and exhibits enhanced collective fluctuations. We analyze fluctuation effects in the quantum critical regime near a d-wave Pomeranchuk instability in two dimensions. Density correlations with a d-wave form factor and the dynamical forward scattering interaction diverge near the instability. The singular forward scattering leads to large self-energy contributions, which destroy Fermi liquid behavior over the whole Fermi surface except at “cold spots” on the Brillouin zone diagonal. The decay rate of single-particle excitations, which is related to the width of the peaks in the spectral function, exceeds the excitation energy in the low-energy limit. The dispersion of the spectra flattens strongly near those portions of the Fermi surface which are remote from the zone diagonal. The decay rate for DC transport is linear in temperature except at the cold spots. We discuss the possible relevance of d-wave Fermi surface fluctuations for the “strange metal” behavior observed in the normal phase of cuprates.
We compute the spectral density in the normal phase of an interacting homogenous Fermi gas using a TTT-matrix approximation. We fit the quasiparticle peaks of the spectral density to BCS-like dispersion relations and extract estimates of a ``pseudogap'' energy scale and an effective Fermi wave vector as a function of interaction strength. We find that the effective Fermi wave vector of the quasiparticles vanishes when the inverse scattering length exceeds some positive threshold. We also find that, near unitarity, the quasiparticle lifetimes, estimated from the widths of the peaks in the spectral density, approach values on the order of the inverse Fermi energy. These results are consistent with the ``breakdown of Fermi-liquid theory'' observed in recent experiments.
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