Daniel Nagaj, Slovak Academy of Sciences
Abstract
How much entanglement can there be in a ground state of a simple 1D system with local interactions? Critical behavior (e.g. long-range correlations) is usually associated with frustration. When a system is unfrustrated (all local Hamiltonian terms are minimized), we expect the ground state to be simple. While this holds for qubits, things are quite different for higher-spin particles (already for qutrits). We'll talk about a state made from well bracketed words and look at the proof of its high entanglement entropy scaling and a lower bound of the Hamiltonian using congestion in graphs, parenting trees, many uses of the projection lemma and other fun stuff.
Joint work with Sergey Bravyi, Libor Caha, Ramis Movassagh and Peter Shor, http://lanl.arxiv.org/abs/1203.5801