Interaction-enhanced nesting in spin-fermion and Fermi-Hubbard models

The spin-fermion (SF) model postulates that the dominant coupling between low-energy fermions in near critical metals is mediated by collective spin fluctuations (paramagnons) peaked at the Néel wave vector, ${\mathbf{Q}}_N$, connecting hot spots on opposite sides of the Fermi surface. It has been argued that strong correlations at hot spots lead to a Fermi surface deformation (FSD) featuring flat regions and increased nesting. This conjecture was confirmed in the perturbative self-consistent calculations when the paramagnon propagator dependence on momentum deviation from ${\mathbf{Q}}_N$ is given by ${\chi }^{-1}\propto \left|\mathrm{\Delta }q\right|$. Using diagrammatic Monte Carlo (diagMC) technique we show that such a dependence holds only at temperatures orders of magnitude smaller than any other energy scale in the problem, indicating that a different mechanism may be at play. Instead, we find that a ${\chi }^{-1}\propto {\left|\mathrm{\Delta }q\right|}^2$ dependence yields a robust finite-$T$ scenario for achieving FSD. To link phenomenological and microscopic descriptions, we applied the connected determinant diagMC method to the $(t-t^{\prime })$ Hubbard model and found that at large $U/t>5.5$ before the formation of electron and hole pockets (i) the FSD defined as a maximum of the spectral function is not very pronounced; instead, it is the lines of zeros of the renormalized dispersion relation that deforms toward nesting, and (ii) the static spin susceptibility is well described by ${\chi }^{-1}\propto {\left|\mathrm{\Delta }q\right|}^2$. Flat FS regions yield a nontrivial scenario for realizing a non-Fermi liquid state.