Excitation spectra and rank tomography of finite MPS tangent spaces
The work develops a tangent-space method to study excitation spectra of non-uniform quantum systems described by Matrix Product States (MPS). It defines this space as a projective variety constrained by rank conditions on tensor flattenings. The paper introduces particle-number resolved Schmidt-rank distribution (PRSR) to quantify how the expressivity and parametric deficiency of this tangent space vary across different particle sectors.