Excitation spectra and rank tomography of finite MPS tangent spaces
Abstract
We formulate the matrix product state (MPS) tangent-space excitation construction for finite, non-uniform systems with open boundary conditions, using the smooth full-rank stratum of the MPS variety as the variational manifold. The resulting linear tangent ansatz yields a projected-Hamiltonian eigenproblem for approximating excitation spectra. We further introduce a rank tomography that characterizes the particle-sector expressivity of the MPS tangent space. For number-conserving systems, we resolve the Schmidt ranks of reference states by particle number and derive an explicit relation between the resulting rank profile and the dimensions of the tangent-space sectors. This allows sector completeness and parametric deficiency to be determined directly from the reference state, without explicitly constructing a tangent basis, and provides a direct diagnostic of the sectorwise expressivity of the MPS excitation ansatz. We benchmark the finite-system construction on Bose--Hubbard chains against exact diagonalization, finding accurate low-lying excitation branches while identifying sector-dependent limitations of the linear tangent ansatz.
Related
- Radial Excitation Spectra of Light Pseudoscalar and Vector Mesons in Light-Front Holographic QCD
- Beyond Bond Gauge: Exact Tensor-Network Tangent Spaces at Weighted Graph States
- Dijet hadrochemistry: tomography of jet-induced medium excitation and diffusion wake
- Electronic-Structure Control of Nuclear Excitation by Electron Capture in Finite-Density 229Th
- Finite-Temperature Transconductance of Multiterminal Josephson Junctions with Topological Andreev Spectra
BibTeX
@misc{schmidt2026excitation,
title = {{Excitation spectra and rank tomography of finite MPS tangent spaces}},
author = {Otto T. P. Schmidt and Iacopo Carusotto},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2607.05269},
eprint = {2607.05269},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2607.05269},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Excitation spectra and rank tomography of finite MPS tangent spaces
AU - Otto T. P. Schmidt
AU - Iacopo Carusotto
PY - 2026
DA - 2026/10/07
PB - arXiv
DO - 10.48550/arxiv.2607.05269
UR - https://arxiv.org/abs/2607.05269
AB - We formulate the matrix product state (MPS) tangent-space excitation construction for finite, non-uniform systems with open boundary conditions, using the smooth full-rank stratum of the MPS variety as the variational manifold. The resulting linear tangent ansatz yields a projected-Hamiltonian eigenproblem for approximating excitation spectra. We further introduce a rank tomography that characterizes the particle-sector expressivity of the MPS tangent space. For number-conserving systems, we resolve the Schmidt ranks of reference states by particle number and derive an explicit relation between the resulting rank profile and the dimensions of the tangent-space sectors. This allows sector completeness and parametric deficiency to be determined directly from the reference state, without explicitly constructing a tangent basis, and provides a direct diagnostic of the sectorwise expressivity of the MPS excitation ansatz. We benchmark the finite-system construction on Bose--Hubbard chains against exact diagonalization, finding accurate low-lying excitation branches while identifying sector-dependent limitations of the linear tangent ansatz.
ER -