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. We study the interplay of such fragmentation with symmetries, focusing on charge conserving systems with charge conjugation and translation symmetries as a concrete example. The non-Abelian algebra of these symmetries and the projectors onto the fragmented subsectors leads to the emergence of exponentially many logical qubits encoded in degenerate pairs of eigenstates, which can be highly entangled. This algebra also provides necessary conditions for experimental signatures of Hilbert-space fragmentation, such as the persistence of density imbalances at late times.