简介: |
In recent years, fracton phases have expanded our understanding of phases of matter, paralleled by advancements in quantum error correction through quantum low-density parity check (qLDPC) codes, including asymptotically good quantum codes typically crafted via product code approaches. Despite some overlap between qLDPC code dimension and fracton ground state degeneracy scaling behaviors, the usual geometric locality of fractons versus the k-locality of generic codes posed a challenge. This talk addresses the challenge by introducing a set of conditions for classical input codes in product construction that, when met, yield fracton order in the resulting quantum codes. We'll illustrate how a particular fracton model on nonlocal graphs meets these conditions only occasionally, and propose a family of product codes which typically realize nonlocal fractons. Additionally, by introducing geometric locality into our framework, we bridge our new fracton order definition with established fracton phase concepts, employing two-dimensional local classical codes derived from pinwheel tiling—an approach that pushes the boundaries of geometrically local codes. The quantum stabilizer models derived from such codes can host either Type-I or Type-II fracton order.
|