SMuK 2023 – scientific programme
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HK: Fachverband Physik der Hadronen und Kerne
HK 71: Structure and Dynamics of Nuclei XVI
HK 71.2: Talk
Thursday, March 23, 2023, 16:15–16:30, SCH/A117
Eigenvector continuation for the pairing Hamiltonian — •Margarida Companys Franzke1, Alexander Tichai1,2,3, Kai Hebeler1,2,3, and Achim Schwenk1,2,3 — 1Technische Universität Darmstadt, Department of Physics — 2ExtreMe Matter Institute EMMI, GSI Helmholtzzentrum für Schwerionenforschung GmbH — 3Max-Plank Institut für Kernphysik, Heidelberg
The design of emulation techniques for the evaluation of many-body observables is attracting increasing attention over the past years. In particular the framework of eigenvector continuation (EC) has been identified as a powerful tool if the Hamiltonian admits for a parametric dependence. By training the emulator on a set of training data the many-body solution for arbitrary parameter values can be robustly predicted in many cases. Furthermore, it can be used to resum perturbative expansions. In this work, we apply EC to the pairing Hamiltonian and show that i) EC-resummed perturbation theory is in qualitative agreement with the exact solution and ii) EC-based emulators robustly predict the ground-state energy once the training data are chosen appropriately. In particular the phase transition from a normal to a superfluid regime is quantitatively predicted from a very low number of training points. Finally the use of approximate training data is discussed and how many-body truncations may affect the emulator's performance.
Funded by the ERC Grant Agreement No. 101020842.