IAS Physics Group Meeting

Abstract: It is well-known that the Hilbert space of a quantum field theory does not factor into a tensor product of degrees of freedom in a region and its complement. Nevertheless, the split property guarantees that there exists a factorization such that the degrees of freedom between two regions separated by an arbitrarily small distance act on different factors.

In this talk, I will discuss whether this splitting can be performed simultaneously at infinitely many locations, addressing the question of a bijective locality-preserving embedding of the algebra of observables of a field theory into the algebra of a lattice system with infinite-dimensional on-site Hilbert spaces. For 1+1d theories, I will argue that the gravitational anomaly provides a fundamental obstruction to the existence of such an embedding. I will also explain how it can be used to construct non-trivial quantum cellular automata on 2d lattice systems with infinite-dimensional on-site Hilbert spaces, which is known to be impossible for spin systems.