Partial transpose is a useful operation in quantum many-body systems, that can be used to detect quantum entanglement. For example, it can beused to define a quantum entanglement measure -- entanglement negativity -- that can detect quantum correlation in mixed quantum states. In this talk, I will describe how partial transpose can be used to detect topology and entanglement in quantum many-body systems. First, I will introduce our constructions of many-body topological invariants for topological insulators and superconductors using partial transpose. One of the key technological steps for this purpose is to define/introduce partial transpose properly. Second, I will discuss entanglement negativity in holographic models of quantum many-body systems ranging from tensor network models to AdS/CFT. In particular, I will discuss its connection to geometrical objects in the bulk -- the so-called entanglement wedges, and their cross sectional areas.
Speaker: Shinsei Ryu, Univ. of Chicago
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