Entanglement in the quantum Ising model

Understand

We study the asymptotic scaling of the entanglement of a block of spins for the ground state of the one-dimensional quantum Ising model with transverse field.

• When the field is sufficiently strong, the entanglement grows at most logarithmically in the number of spins.
• The proof utilises a transformation to a model of classical probability called the continuum random-cluster model, and is based on a property of the latter model termed ratio weak-mixing.
• Our proof applies equally to a large class of disordered interactions.