Relative signs of tunnel couplings in the double quantum dot Hamiltonian

Determine the physically correct relative signs of the eight unique tunnel couplings t11, t12, t21, t22 (singlet subspace) and t31, t32, t41, t42 (triplet subspace) in the 15×15 Hubbard-like Hamiltonian that models the Si/SiGe double quantum dot measured via delta-axis spectroscopy, accounting for multi-electron interactions and excited orbital states that make these signs ambiguous.

Background

The paper introduces delta-axis spectroscopy (DAXS) to map the energy spectrum of a Si/SiGe double quantum dot and fit a 15×15 Hamiltonian with singlet and triplet subspaces. Extracting tunnel couplings requires specifying both magnitudes and signs, but the authors note that the relative signs of the couplings are not directly known due to the complexity of multi-electron interactions and excited orbital states.

To proceed, the analysis constrains all tunnel couplings to be positive and then evaluates the impact of different sign combinations, showing that certain sign choices form equivalence classes and that fitted magnitudes vary by up to ~20% for some couplings. Nevertheless, the actual physical sign configuration remains unresolved, and determining it would remove a systematic ambiguity in parameter extraction and model identification.