16:00
Quantum cellular automata and invertible phases of matter
Abstract
Quantum cellular automata describe discrete-time dynamics of quantum lattice systems which have a causal light-cone. They can be mathematically characterized as the group of bounded-spread automorphisms of the quasi-local C*-algebra associated to the lattice system. Invertible phases are a class of topological phases of matter with no bulk anyon content, and are mathematically described by a class of states on the quasi-local algebra C*-algebra which have a stable inverse under stacking, which form a group. We will show that in any spatial dimension, if the local Hilbert spaces of the lattice system are infinite dimensional, the group of stable equivalence classes of quantum cellular automata and the group of invertible phases are isomorphic . We will then explain the construction of a large class of non-trivial examples on the 2D lattice from holomorphic conformal nets. This talk is geared toward operator algebraists and will require no knowledge of physics. Based on joint work Nikita Sopenko and Ryan Thorngren.