Passive error correction protects logical information forever (in the thermodynamic limit) by
updating the system based only on local information and few-body interactions. A …

We prove the existence of extensive many-body Hamiltonians with few-body interactions
and a many-body mobility edge: all eigenstates below a nonzero energy density are …

Recent generalizations of symmetry have refortified the power of symmetry to non-
perturbatively characterize the dynamics and phases of many-body systems [1–4]. The crux …

We explore the rich landscape of higher-form and non-invertible symmetries that emerge at
low energies in generic ordered phases. Using that their charge is carried by homotopy …

We introduce a family of local models of dynamics based on “word problems” from computer
science and group theory, for which we can place rigorous lower bounds on relaxation …

We investigate the phenomenon of Hilbert space fragmentation (HSF) in open quantum
systems and find that it can stabilize highly entangled steady states. For concreteness, we …

We introduce a large class of models exhibiting robust ergodicity breaking in quantum
dynamics. Our work is inspired by recent discussions of “topologically robust Hilbert space …

We present a mathematical theory of metastable pure states in closed many-body quantum
systems with finite-dimensional Hilbert space. Given a Hamiltonian, a pure state is defined to …

Symmetry algebras of quantum many-body systems with locality can be understood using
commutant algebras, which are defined as algebras of operators that commute with a given …

By mapping the calculation of Mazur bounds to the enumeration of walks on fractal
structures, we present exact bounds on the late-time behavior of spin autocorrelation …