Fractons are a new type of quasiparticle which are immobile in isolation, but can often move
by forming bound states. Fractons are found in a variety of physical settings, such as spin …

Fractons emerge from many-body systems, featuring subdimensional particles with
restricted mobility. These particles have attracted interest for their roles across disciplines …

We introduce a new kind of foliated quantum field theory (FQFT) of gapped fracton orders in
the continuum. FQFT is defined on a manifold with a layered structure given by one or more …

A bstract We generalize the idea of symmetry topological field theory (SymTFT) for
subsystem symmetry. We propose the 2-foliated BF theory with level N in (3+ 1) d as …

Fracton phases exhibit striking behavior which appears to render them beyond the standard
topological quantum field theory (TQFT) paradigm for classifying gapped quantum matter …

We investigate how symmetry and topological order are coupled in the (2+ 1)–dimensional
ZN rank-2 toric code for general N, which is an exactly solvable point in the Higgs phase of a …

Quantum computers require memories that are capable of storing quantum information
reliably for long periods of time. The surface code is a two-dimensional quantum memory …

We study p-string condensation mechanisms for fracton phases from the viewpoint of higher-
form symmetry, focusing on the examples of the X-cube model and the rank-two symmetric …

We introduce a class of intrinsic symmetry-protected topological mixed state (mSPT) in open
quantum systems that feature modulated symmetries, such as dipole and subsystem …

Fracton order is an intriguing new type of order which shares many common features with
topological order, such as topology-dependent ground-state degeneracies, and excitations …