We review the mathematical speed limits on quantum information processing in many-body
systems. After the proof of the Lieb–Robinson Theorem in 1972, the past two decades have …

Although condensed matter systems usually do not have higher-form symmetries, we show
that, unlike 0-form symmetry, higher-form symmetries can emerge as exact symmetries at …

Distinguishing whether a system supports alternate low-energy (locally stable) states—
stable (true vacuum) versus metastable (false vacuum)—by direct observation can be …

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 …

We rigorously show that a local spin system giving rise to a slow Hamiltonian dynamics is
stable against generic, even time-dependent, local perturbations. The sum of these …

Phases of matter with robust ground-state degeneracy, such as the quantum toric code, are
known to be capable of robust quantum information storage. Here, we address the converse …

Symmetry-protected topological phases cannot be described by any local order parameter
and are beyond the conventional symmetry-breaking paradigm for understanding quantum …

We show that it is possible to perform Heisenberg-limited metrology on GHZ-like states, in
the presence of generic spatially local, possibly strong interactions during the measurement …

We introduce a notion of a\emph {local gap} for interacting many-body quantum lattice
systems and prove the validity of response theory and Kubo's formula for localized …