Symmetry-protected topological scar subspaces

TL;DR

This paper introduces the concept of symmetry-protected topological (SPT) scar subspaces in quantum many-body scars, extending topological protection beyond ground states to special non-thermal eigenstates, demonstrated using the AKLT model.

Contribution

It defines SPT scar subspaces stabilized by a restricted spectrum-generating algebra and symmetries, showing they inherit topological properties from ground states, expanding the understanding of topological phases.

Findings

SPT scar subspaces retain topological properties of ground states.

AKLT model's bimagnon scar subspace exhibits topological order.

Scar subspaces can modify and inherit topological features systematically.

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.