Matrix Product States with long-range Localizable Entanglement

Abstract

We derive a criterion to determine when a translationally invariant matrix product state (MPS) has long-range localizable entanglement, where that quantity remains finite in the thermodynamic limit. We give examples fulfilling this criterion and eventually use it to obtain all such MPS with bond dimension 2 and 3.

8 pages, 1 figure

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• Locality and nonlocality of classical restrictions of quantum spin systems with applications to quantum large deviations and entanglement
• Preparing matrix product states via fusion: constraints and extensions
• Classical restrictions of generic matrix product states are quasi-locally Gibbsian
• Non-onsite symmetries and quantum teleportation in split-index matrix product states
• Tensor network states for the description of quantum many-body systems