Fine-grained entanglement loss along renormalization-group flows

We explore entanglement loss along renormalization group trajectories as a basic quantum information property underlying their irreversibility. This analysis is carried out for the quantum Ising chain as a transverse magnetic field is changed. We consider the ground-state entanglement between a larg...

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Bibliographic Details
Published in:Physical review. A, Atomic, molecular, and optical physics Atomic, molecular, and optical physics, 2005-03, Vol.71 (3), Article 034301
Main Authors: Latorre, J. I., Lütken, C. A., Rico, E., Vidal, G.
Format: Article
Language:English
Subjects:
ATOMIC AND MOLECULAR PHYSICS
CORRELATIONS
DENSITY MATRIX
EIGENVALUES
GROUND STATES
HAMILTONIANS
INFORMATION THEORY
MAGNETIC FIELDS
MATERIALS SCIENCE
QUANTUM MECHANICS
RENORMALIZATION
SPIN
TRAJECTORIES
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Summary:We explore entanglement loss along renormalization group trajectories as a basic quantum information property underlying their irreversibility. This analysis is carried out for the quantum Ising chain as a transverse magnetic field is changed. We consider the ground-state entanglement between a large block of spins and the rest of the chain. Entanglement loss is seen to follow from a rigid reordering, satisfying the majorization relation, of the eigenvalues of the reduced density matrix for the spin block. More generally, our results indicate that it may be possible to prove the irreversibility along renormalization group trajectories from the properties of the vacuum only, without need to study the whole Hamiltonian.
ISSN:1050-2947
1094-1622
DOI:10.1103/PhysRevA.71.034301