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 …

Fracton phases constitute a new class of quantum state of matter. They are characterized by
excitations that exhibit restricted mobility, being either immobile under local Hamiltonian …

Symmetry plays a central role in quantum field theory. Recent developments include
symmetries that act on defects and other subsystems, and symmetries that are categorical …

Quantum error correction is an indispensable ingredient for scalable quantum computing. In
this Perspective we discuss a particular class of quantum codes called “quantum low-density …

A fundamental distinction between many-body quantum states are those with short-and long-
range entanglement (SRE and LRE). The latter cannot be created by finite-depth circuits …

We show that the combination of charge and dipole conservation—characteristic of fracton
systems—leads to an extensive fragmentation of the Hilbert space, which, in turn, can lead …

We show how a finite number of conservation laws can globally “shatter” Hilbert space into
exponentially many dynamically disconnected subsectors, leading to an unexpected …

We introduce a generalization of conventional lattice gauge theory to describe fracton
topological phases, which are characterized by immobile, pointlike topological excitations …

We study complex scalar theories with dipole symmetry and uncover a no-go theorem that
governs the structure of such theories and which, in particular, reveals that a Gaussian …

We introduce new classes of hydrodynamic theories inspired by the recently discovered
fracton phases of quantum matter. Fracton phases are characterized by elementary …