Symmetry Fragmentation

In quantum many-body systems with kinetically constrained dynamics, the Hilbert space can split into exponentially many disconnected subsectors, a phenomenon known as Hilbert-space fragmentation. These subsectors can be viewed as protecting classical information about the initial state. We show that the interplay of fragmentation with symmetries enables the protection of quantum information. Focusing on charge conserving systems with charge conjugation and translation symmetries, we show that the nontrivial action of these symmetries on the fragmented subsectors generates exponentially many logical qubits encoded in degenerate pairs of eigenstates, which can be highly entangled. This symmetry action also provides necessary conditions for experimental signatures of Hilbert-space fragmentation, such as the persistence of density imbalances at late times.