Interaction-enhanced nesting in Spin-Fermion and Fermi-Hubbard models

TL;DR

This paper investigates the mechanisms behind Fermi surface deformation and nesting in spin-fermion and Hubbard models, revealing that a quadratic dependence of spin susceptibility on momentum deviation is key to finite-temperature nesting.

Contribution

It demonstrates that the commonly assumed linear dependence of susceptibility on momentum deviation is invalid at finite temperatures, proposing a quadratic dependence as a more robust mechanism for Fermi surface nesting.

Findings

The linear dependence of susceptibility holds only at extremely low temperatures.

A quadratic dependence of susceptibility on momentum deviation supports finite-temperature Fermi surface nesting.

Fermi surface deformation occurs before electron and hole pocket formation at high interaction strengths.

Abstract

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 N\'{e}el wave vector, ${\bf Q}_N$, 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 ${\bf Q}_N$ is given by $\chi^{-1} \propto |\Delta q|$. 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 $\chi^{-1} \propto |\Delta q|^{2}$ 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 $(t-t')$ Hubbard model and found that in this case: (i) the FSD is not very pronounced, and, instead, it is the lines of zeros of the renormalized dispersion relation that deform towards nesting; (ii) this phenomenon appears at large $U/t>5.5$ before the formation of electron and hole pockets; (iii) the static spin susceptibility is well described by $\chi^{-1} \propto |\Delta q|^{2}$. Flat FS regions yield a non-trivial scenario for realizing a non-Fermi liquid state.