Thermal form-factor series for dynamical correlation functions of quantum integrable models

• Applicant: Professor Dr. Frank Göhmann
• Subject Area: Theoretical Condensed Matter Physics
• Term: since 2024
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 545565024

The main objective of our proposal is a complete understanding of the dynamical correlation functions of the Heisenberg-Ising chain in equilibrium with a thermostat or after the relaxation following a quantum quench. For this purpose we shall study exact series representations of the correlation functions based on a so-called thermal form factor expansion. The latter will make it possible to compute the correlation functions with high precision and to compare them with experimental data obtained, e.g., in neutron scattering or cold-atom experiments. Our method exploits the integrable structure of the Heisenberg-Ising chain. As opposed to complementary numerical or perturbative approaches it will allow us to access certain universal features of the system showing up, e.g., in the asymptotic behavior of the correlation functions for long times or at large distances. Our closed analytic formulae will provide information for an interpretation of the experiments and, at the same time, make it possible to estimate the errors of the more universally applicable, but typically less powerful purely numerical methods.

• DFG Programme: Research Grants
• International Connection: France
• Partner Organisation: Agence Nationale de la Recherche / The French National Research Agency
• Cooperation Partner: Professor Dr. Karol Kozlowski