Implementing superconducting corrections to the ground state Hamiltonian in MeanFi
Jasper Brookman (TU Delft - Applied Sciences)
A.R. Akhmerov – Mentor (TU Delft - Applied Sciences)
A.L. Rigotti Manesco – Mentor (TU Delft - Applied Sciences)
R.J.Z. Zijderveld – Mentor (TU Delft - Applied Sciences)
A.R. Akhmerov – Graduation committee member (TU Delft - Applied Sciences)
S. Goswami – Graduation committee member (TU Delft - QRD/Goswami Lab)
C.K. Andersen – Graduation committee member (TU Delft - QRD/Andersen Lab)
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Abstract
Understanding the ground-state properties of many-body systems is a computational challenge in condensed-matter physics. MeanFi is a Python package that performs self-consistent Hartree-Fock calculations on non-superconducting tight-binding models and aims to find the ground state solution of a Hamiltonian with density-density interactions. This thesis presents how this package is generalized to also perform these calculations for superconducting tight-binding models. First, a complete derivation of the mean-field expansion is given by applying Wick’s contractions and the mean-field approximation. This expansion is then transformed into the Bogoliubov-de Gennes basis to explicitly include superconducting terms in the Hamiltonian. Second, the self-consistency criterion is adapted by constraining the solution space by enforcing symmetries on the solution by using Qsymm. Third, finite-temperature calculations are added to the algorithm and the total charge of the system replaces the electron filling-factor that was used in MeanFi, introducing a minimization problem to the algorithm. Last, the updated algorithm is applied to a 1D-Hubbard model with attractive interactions and the resulting superconducting gap as a function of temperature matches theoretical predictions from BCS-theory.