Fragmented topological excitations in generalized hypergraph product codes
Phys. Rev. B 114, 225110 – Published 6 October, 2026
DOI: https://doi.org/10.1103/8vmg-v4dq
Abstract
Quantum stabilizer codes serve as a promising paradigm for realizing fault-tolerant quantum computation, and their natural mapping to the ground states of exactly solvable spin models strongly motivates the exploration of many-body orders within these systems. In this work, we investigate the fracton topological orders in a specific family of codes derived from a recently proposed general construction. This particular code family can be understood as a class of generalized hypergraph product codes, and we term the corresponding exactly solvable spin models orthoplex models based on the geometry of their stabilizers. In three dimensions, the orthoplex model exhibits a series of intriguing properties, including non-Abelian lattice defects and a nonmonotonic ground-state degeneracy as a function of system size. Most remarkably, in four dimensions we discover fragmented topological excitations: while manifesting as discrete, isolated points in real space, their projections onto lower-dimensional subsystems form connected objects such as loops, thereby revealing their intrinsic topological nature. Consequently, these fragmented excitations constitute an intriguing intermediate class between pointlike and spatially extended topological excitations. More broadly, these rich features establish the underlying general construction framework of stabilizer codes as a versatile and analytically tractable platform for studying many-body orders.
