A converse to Lieb-Robinson bounds in one dimension using index theory

Understand

Unitary dynamics with a strict causal cone (or "light cone") have been studied extensively, under the name of quantum cellular automata (QCAs).

• In particular, QCAs in one dimension have been completely classified by an index theory.
• Physical systems often exhibit only approximate causal cones; Hamiltonian evolutions on the lattice satisfy Lieb-Robinson bounds rather than strict locality.
• This motivates us to study approximately locality preserving unitaries (ALPUs).