Competition between adiabatic phonons and Kohn-anomaly-driven quantum criticality

Determine the temperature scale, if one exists, below which adiabatic phonons can effectively compete with Kohn-anomaly-driven quantum criticality in the three-dimensional Hubbard-Holstein model, and characterize the corresponding connections to disordered systems modeled using cluster extensions of dynamical mean-field theory.

Background

The paper studies the antiferromagnetic quantum-critical regime of the three-dimensional Hubbard-Holstein model using dynamical-$U$ ladder-D$Gamma$A. For the simple-cubic lattice and the parameter range investigated, lines of Kohn points determine the nonanalytic temperature dependence of the magnetic susceptibility and produce a parabolic dependence of the Néel temperature on doping.

The authors find that even for their most adiabatic phonons, with characteristic frequency $\omega_0=0.1$, the DMFT self-energy retains Fermi-liquid behavior and does not generate finite zero-temperature quasiparticle scattering capable of destroying the Kohn-point-driven Fermi-surface geometry. It remains unresolved whether sufficiently low temperatures could nevertheless allow adiabatic phonons to overcome this mechanism, and how such behavior would compare with disordered-system physics accessible through cluster extensions of DMFT.