Fracton topological phases host fractionalized excitations that are either completely immobile or only mobile along certain lines or planes. We demonstrate how such phases can be understood in terms of two fundamentally different types of parton constructions, in which physical degrees of freedom are decomposed into clusters of “parton” degrees of freedom subject to emergent gauge constraints. First, we employ noninteracting partons subject to multiple overlapping constraints to describe a fermionic fracton model. Second, we demonstrate how interacting partons can be used to develop new models of bosonic fracton phases, both with string and membrane logical operators (type-I fracton phases) and with fractal logical operators (type-II fracton phases). In particular, we find a new type-II model, which saturates a bound on its information storage capacity. Our parton approach is generic beyond exactly solvable models and provides a variational route to realizing fracton phases in more physically realistic systems.

• Received 19 March 2017

DOI:https://doi.org/10.1103/PhysRevB.96.165105