Hierarchical Reduction of Invariant Subspaces: From Fragmentation to Many-Body Scars
Abstract
We investigate a hierarchy of invariant Hilbert-space structures connecting Hilbert-space fragmentation, partial solvability, and quantum many-body scars. For spin chains with fragmented spin-1/2 subspaces and their local deformations, we show, using the spin-$1$ XXC chain as a representative example, how successive local deformations reduce extensive irreducible-string fragmentation through an implicitly embedded spin-1/2 invariant space and ultimately to a single scar tower, connecting the XXC, perturbed XXC, and spin-$1$ XY scar models. Through the intermediate embedded space, local dynamics couples states from distinct frozen irreducible-string sectors and selects a new decomposition into representations, from which smaller invariant spaces can be retained. We also establish a rigidity constraint on isolating nonsymmetric towers and a constructive correspondence that transfers a reduction between locally realizable representations of the embedded dynamics. The latter demonstrates that the reduction hierarchy can be transferred through a unitary transformation within the embedded subspace, yielding an exact scar tower built on a Néel reference state without requiring unitary equivalence of the full Hamiltonians.
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BibTeX
@misc{matsui2026hierarchical,
title = {{Hierarchical Reduction of Invariant Subspaces: From Fragmentation to Many-Body Scars}},
author = {Chihiro Matsui},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.30597},
eprint = {2610.30597},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.30597},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Hierarchical Reduction of Invariant Subspaces: From Fragmentation to Many-Body Scars
AU - Chihiro Matsui
PY - 2026
DA - 2026/10/22
PB - arXiv
DO - 10.48550/arxiv.2610.30597
UR - https://arxiv.org/abs/2610.30597
AB - We investigate a hierarchy of invariant Hilbert-space structures connecting Hilbert-space fragmentation, partial solvability, and quantum many-body scars. For spin chains with fragmented spin-1/2 subspaces and their local deformations, we show, using the spin-$1$ XXC chain as a representative example, how successive local deformations reduce extensive irreducible-string fragmentation through an implicitly embedded spin-1/2 invariant space and ultimately to a single scar tower, connecting the XXC, perturbed XXC, and spin-$1$ XY scar models. Through the intermediate embedded space, local dynamics couples states from distinct frozen irreducible-string sectors and selects a new decomposition into representations, from which smaller invariant spaces can be retained. We also establish a rigidity constraint on isolating nonsymmetric towers and a constructive correspondence that transfers a reduction between locally realizable representations of the embedded dynamics. The latter demonstrates that the reduction hierarchy can be transferred through a unitary transformation within the embedded subspace, yielding an exact scar tower built on a Néel reference state without requiring unitary equivalence of the full Hamiltonians.
ER -