Exponential decay of quantum conditional information in thermal states of 1D short-ranged gapped Hamiltonians.

Math Physics Seminar
Friday, April 19, 2019 - 4:00pm for 1 hour (actually 50 minutes)
Skiles 005
Pavel Svetlichnyy – School of Physics, GaTeach – psvetlichny3@gatech.edu
Federico Bonetto

I will talk about a conjecture that in Gibbs states of one-dimensional spin chains with short-ranged gapped Hamiltonians the quantum conditional mutual information (QCMI) between the parts of the chain decays exponentially with the length of separation between said parts. The smallness of QCMI enables efficient representation of these states as tensor networks, which allows their efficient construction and fast computation of global quantities, such as entropy. I will present the known partial results on the way of proving of the conjecture and discuss the probable approaches to the proof and the obstacles that are encountered.