Entanglement in the quantum Ising model

Abstract

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.

References in corpus (5)

• Scaling of Entanglement close to a Quantum Phase Transitions
• Entanglement in a simple quantum phase transition
• Matrix product states represent ground states faithfully
• Entanglement entropy of random quantum critical points in one dimension
• Increasing of entanglement entropy from pure to random quantum critical chains

Cited by in corpus (7)

• Area laws for the entanglement entropy - a review
• Entanglement Transition in the Projective Transverse Field Ising Model
• The phase transition of the quantum Ising model is sharp
• Quantum critical behavior of the quantum Ising model on fractal lattices
• Bounded entanglement entropy in the quantum Ising model
• Uniform bound of the entanglement for the ground state of the quantum Ising model with large transverse magnetic field
• Genuine $k$-partite correlations and entanglement in the ground state of the Dicke model for interacting qubits