Symmetry-protected topological scar subspaces

• URL: http://arxiv.org/abs/2512.11216v1
• Date: Fri, 12 Dec 2025 01:48:36 GMT
• Title: Symmetry-protected topological scar subspaces
• Authors: Chihiro Matsui, Thomas Quella, Naoto Tsuji,
• Abstract summary: We introduce the concept of a symmetry-protected topological (SPT) scar subspace.<n> QMBS often admit a non-interacting quasiparticle description.<n>We show that QMBS do not necessarily retain the protecting symmetries of the Hamiltonian.
• Score: 0.4588028371034407
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We propose a framework that extends the notion of symmetry-protected topological properties beyond the ground-state paradigm to dynamically isolated subspaces formed by exceptional non-thermal energy eigenstates of non-integrable systems, known as quantum many-body scars (QMBS). We introduce the concept of a symmetry-protected topological (SPT) scar subspace -- a Hilbert subspace stabilized by a restricted spectrum-generating algebra (rSGA) while being protected by on-site, inversion, and time-reversal symmetries. QMBS often admit a non-interacting quasiparticle description, which enables matrix-product representations with small bond dimension. Although individual QMBS do not necessarily retain the protecting symmetries of the Hamiltonian, we show that the subspace formed by the symmetry-connected QMBS does retain them, giving rise to consistently emerging topological properties across the entire scar subspace. Using the spin-$1$ Affleck--Kennedy--Lieb--Tasaki (AKLT) model, we demonstrate that its bimagnon scar subspace reflects the topological properties of the SPT ground state, as evidenced by the appropriate bond-space symmetry representations, the expected topological response, and the numerically verified long-range string order. Our findings indicate that scar subspaces can inherit -- and in inhomogeneous cases systematically modify -- the topological character of the SPT ground state, offering a new and experimentally accessible platform for probing symmetry-protected topology beyond the ground-state regime.

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