Topology and entanglement detected by partial transpose

Monday, October 15, 2018 - 2:30pm

Partial transpose is a useful operation in quantum many-body systems,
that can be used to detect quantum entanglement. For example, it can be
used 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.

3 Le Conte Hall- UCB
University of Chicago