Spin and charge excitations across the phase diagram of the 2D Hubbard model.

Leveraging the power of algorithmic Matsubara integration (AMI) we can generate pseudo-analytic results for virtually any diagrammatic expansion. We generate the longitudinal spin and charge susceptibilities for the 2D Hubbard model and employ our AMI toolset to obtain expressions that are explicit functions of chemical potential, temperature, interaction strength and frequency (both real and Matsubara).

We study the weak coupling limit for finite next-nearest neighbour hopping where we resolve features in real frequency spectra that appear to be missed in numerical analytic continuation of Matsubara axis data. We track these features throughout the phase diagram and find that their existence has a simple explanation made clear when considering the $chi_{uparrowuparrow}$ and $chi_{uparrowdownarrow}$ susceptibilities. We further find that incompressibility in the model at weak coupling originates from vector nesting near the Lifshitz transition and present evidence that this may be distinct from Mott insulating behaviour.