A recipe for quantum fragmentation

Hilbert-space fragmentation (HSF) provides a robust mechanism for nonergodicity in isolated quantum systems, whereby the Hilbert space shatters into many dynamically disconnected Krylov sectors. Most known examples are essentially “classical,” in the sense that their Krylov sectors are spanned by product-state bases. However, in principle, HSF could also occur in an entangled basis, in which case it is known as quantum fragmentation (QF)—a phenomenon that remains largely unexplored. This raises a number of natural questions.

For instance, since every Hamiltonian is diagonal and therefore trivially “fragmented” in its eigenbasis, what distinguishes genuine quantum fragmentation from this trivial limit? Is there a principled recipe for constructing QF models? Can we systematically label the resulting Krylov sectors? How can QF be experimentally diagnosed and distinguished from classical fragmentation (CF)? And finally, can the notion of QF be meaningfully extended to systems in more than one dimension?

Come to our talk, and you will find out.