Fragmented Topological Excitations in Generalized Hypergraph Product Codes

• URL: http://arxiv.org/abs/2601.09850v1
• Date: Wed, 14 Jan 2026 20:14:46 GMT
• Title: Fragmented Topological Excitations in Generalized Hypergraph Product Codes
• Authors: Meng-Yuan Li, Yue Wu,
• Abstract summary: In this work, we investigate the fracton topological orders in a family of codes obtained by a recently proposed general construction.<n>We term the corresponding exactly solvable spin models textitorthoplex models, based on the geometry of the stabilizers.
• Score: 13.310044694105075
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Product code construction is a powerful tool for constructing quantum stabilizer codes, which serve as a promising paradigm for realizing fault-tolerant quantum computation. Furthermore, the natural mapping between stabilizer codes and the ground states of exactly solvable spin models also motivates the exploration of many-body orders in the stabilizer codes. In this work, we investigate the fracton topological orders in a family of codes obtained by a recently proposed general construction. More specifically, this code family can be regarded as a class of generalized hypergraph product (HGP) codes. We term the corresponding exactly solvable spin models \textit{orthoplex models}, based on the geometry of the stabilizers. In the 3D orthoplex model, we identify a series of intriguing properties within this model family, including non-monotonic ground state degeneracy (GSD) as a function of system size and non-Abelian lattice defects. Most remarkably, in 4D we discover \textit{fragmented topological excitations}: while such excitations manifest as discrete, isolated points in real space, their projections onto lower-dimensional subsystems form connected objects such as loops, revealing the intrinsic topological nature of these excitations. Therefore, fragmented excitations constitute an intriguing intermediate class between point-like and spatially extended topological excitations. In addition, these rich features establish the generalized HGP codes as a versatile and analytically tractable platform for studying the physics of fracton orders.

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