Long-range entangled unitaries and algebras

Speaker: Jeongwan Haah (Stanford University)
Series: Isaac Newton Institute Seminar Series
Note: MMBW03 - Structure of entanglement

We teach entanglement and topological order as properties of bipartite or many-body quantum states. I will explain how unitaries and algebras of physical relevance may exhibit long-range entanglement and ask questions that follow from this perspective. In particular, I will sketch the proof that a specific unitary on a 3d lattice of qubits is not a finite depth unitary circuit but has bounded lightcone. We will encounter an algebra of local operators that is isomorphic to usual tensor product algebras but any such isomorphism must not have lightcone. Further, I will point out that there exists a gapped 1d boundary for the three-fermion topological order in 2d which is believed to always carry a gapless chiral edge mode, revealing a subtle role of the underlying algebra of observables. Time permitting, I will discuss on an intrinsic definition of (entanglement) entropy for states on abstract algebras.