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arXiv:cond-mat/0405344 · Physical Review Letters

Quantum Critical Behavior Near a Density-Wave Instability in an Isotropic Fermi Liquid

Andrey V. Chubukov, Victor M. Galitski, Victor M. Yakovenko

Published Feb 3, 2005• 21 citations
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Abstract

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 ${q}_{c}$. 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 $k$ 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.

DOI
10.1103/physrevlett.94.046404

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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 \ensuremathΣ(k,\ensuremathω)\ensuremath≈\ensuremathΣ(k)\ensuremath{\Sigma}(k,\ensuremath{\omega})\ensuremath{\approx}\ensuremath{\Sigma}(k)\ensuremathΣ(k,\ensuremathω)\ensuremath≈\ensuremathΣ(k) to \ensuremathΣ(k,\ensuremathω)\ensuremath≈\ensuremathΣ(\ensuremathω)\ensuremath{\Sigma}(k,\ensuremath{\omega})\ensuremath{\approx}\ensuremath{\Sigma}(\ensuremath{\omega})\ensuremathΣ(k,\ensuremathω)\ensuremath≈\ensuremathΣ(\ensuremathω), where kkk and \ensuremathω\ensuremath{\omega}\ensuremathω 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 behavior of interacting fermions near a ferromagnetic Stoner instability. We show that the Landau damping of the spin susceptibility is a relevant perturbation near a ferromagnetic quantum-critical point (FQCP). We argue that, as the system approaches FQCP, the fermionic self-energy crosses over from predominantly momentum dependent away from the transition to predominantly frequency dependent in the immediate vicinity of the transition. We argue that due to this self-generated locality, the quasiparticle effective mass does not diverge before FQCP.
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 renormalization of the Fermi-liquid parameters in the vicinity of a density wave quantum phase transition, which should occur in MOSFET systems at low densities. First, using a perturbative RPA treatment of fluctuations, we calculate the electronic self-energy and show that the effective mass diverges at the density wave transition point. Second, we go beyond perturbation theory, making use of the exact Pitaevskii identities. Within this exact analysis, we also find a divergence of the effective mass, which occurs at higher densities in the fluctuation region, as compared to the perturbation theory. This result signals the break-down of conventional Fermi-liquid description in the vicinity of the transition point. The divergence of the effective mass gives rise to a singular behavior of the electronic compressibility. We suggest that the experimentally observed enhancement of the effective mass is a precursor to a second order thermodynamic phase transition into a glassy density wave state.
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We report on numerically exact determinantal quantum Monte Carlo simulations of the onset of spin-density-wave (SDW) order in itinerant electron systems captured by a sign-problem-free two-dimensional lattice model. Extensive measurements of the SDW correlations in the vicinity of the phase transition reveal that the critical dynamics of the bosonic order parameter are well described by a dynamical critical exponent z=2z=2z=2, consistent with Hertz-Millis theory, but are found to follow a finite-temperature dependence that does not fit the predicted behavior of the same theory. The presence of critical SDW fluctuations is found to have a strong impact on the fermionic quasiparticles, giving rise to a dome-shaped superconducting phase near the quantum critical point. In the superconducting state we find a gap function that has an opposite sign between the two bands of the model and is nearly constant along the Fermi surface of each band. Above the superconducting Tc{T}_{c}Tc​, our numerical simulations reveal a nearly temperature and frequency independent self-energy causing a strong suppression of the low-energy quasiparticle weight in the vicinity of the hot spots on the Fermi surface. This indicates a clear breakdown of Fermi liquid theory around these points.
Opportunities for topological phase transitions in strongly correlated Fermi systems near a quantum critical point are explored as an alternative to collective scenarios for experimentally observed departures from standard Fermi-liquid behavior. Attention is focused on a quantum critical point at which the effective mass is divergent due to vanishing of the quasiparticle group velocity at the Fermi surface. Working within the original Landau quasiparticle theory, it is demonstrated that the quasiparticle picture can remain meaningful beyond the quantum critical point through rearrangements of the unstable normal Fermi surface and quasiparticle spectrum. Two possibilities emerge at zero temperature, depending on whether the quasiparticle interaction is regular or singular at zero momentum transfer. In the regular case, one type of topological phase transformation leads to a state with a multiconnected Fermi surface. In the singular case, another type of topological phase transition leads to an exceptional state containing a fermion condensate – the Fermi surface swells into a volume in momentum space, within which partial occupation prevails and quasiparticle energies are pinned to the chemical potential. As the temperature increases from zero to a characteristic value Tm, a crossover can occur from the state with multiple Fermi surfaces to that containing a fermion condensate.