Dynamical susceptibility and quantum Fisher information in the Su-Schrieffer-Heeger model with Hatsugai-Kohmoto interactions
We investigate the dynamical spin and charge susceptibilities and the associated quantum Fisher information in a class of interacting lattice models, with a primary focus on the Su-Schrieffer-Heeger model in the presence of Hatsugai-Kohmoto interactions. To provide a rigorous analytical benchmark, we contrast the response properties of the SSH-HK system with those of the single-band Hubbard and SSH-Hubbard models, treated within the random-phase approximation. While standard Hubbard-type interactions typically suppress excitation strength, we demonstrate that the SSH-HK model displays qualitatively distinct physical behavior arising from the interplay between SSH dimerization and the momentum-diagonal nature of the HK interaction. Leveraging the exact solvability of the HK term, we derive closed-form expressions for the dynamical susceptibility, revealing unique filling-controlled characteristics such as a finite response at zero wave vector and a pronounced restructuring of spectral weight across integer and fractional filling sectors. We show that the quantum Fisher information, defined as the frequency integral of the imaginary part of the susceptibility, serves as an efficient probe of these filling sectors, exhibiting distinct piecewise behavior that distinguishes integer from fractional fillings. Notably, our results indicate that the quantum Fisher information remains insensitive to topological transitions within uniform-density regimes, highlighting the limitations of standard dynamical response functions in characterizing band topology. These findings establish the SSH-HK model as a powerful analytical platform for exploring the competition between topology and strong correlations, demonstrating how dynamical susceptibilities and the quantum Fisher information provide complementary, experimentally accessible probes of many-body physics.