IQI Weekly Seminar
Quantum entanglement, a concept from quantum information theory, has been widely used in condensed matter physics to characterize quantum correlations that are difficult to study using conventional methods. It provides unique insights into the physics of critical states and topological order. It is also quantitatively related to the difficulty of describing ground states using matrix-product-state representations in numerical approximations. In this talk, I will discuss some recent examples in these directions in the context of 1D quantum systems. I will focus on conceptual messages rather than technical perspectives.
Area law: Starting with a review of known rigorous results on the relation between gapped states, correlation decay, area law, and efficient matrix-product-state representations, I will discuss area law for Renyi entropy and possible generalizations in the presence of ground-state degeneracy.
Entanglement and topological order: It is argued that topological order is essentially a pattern of long-range entanglement. I will discuss a quantitative characterization of long-range entanglement using local quantum circuits. In particular, I will show that to generate a topologically ordered state from a product state a local quantum circuit of linear (in system size) depth is necessary and (up to small errors) sufficient.
Entanglement in critical disordered systems: Many-body localization studies how disorder leads to localized states in strongly correlated systems. It is a property associated with all eigenstates (not just the ground state) of disordered systems. I will show how to use entanglement for probing the singularities of all eigenstates.
References:
http://arxiv.org/abs/1403.0327