Fine-grained entanglement loss along renormalization-group flows

J. I. Latorre, C. A. Lütken, E. Rico, and G. Vidal

Phys. Rev. A 71, 034301 – Published 2 March 2005

Abstract

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.

Received 6 May 2004

DOI:https://doi.org/10.1103/PhysRevA.71.034301

Authors & Affiliations

J. I. Latorre¹, C. A. Lütken², E. Rico¹, and G. Vidal³

¹Department d’Estructura i Constituents de la Matèria, University of Barcelona, 08028, Barcelona, Spain
²Department of Physics, University of Oslo, P.O. Box 1048 Blindern, NO-0316 Oslo, Norway
³Institute for Quantum Information, California Institute for Technology, Pasadena, California 91125, USA

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Issue

Vol. 71, Iss. 3 — March 2005

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