Issue
EPL
Volume 81, Number 5, March 2008
Article Number 57003
Number of page(s) 6
Section Condensed Matter: Electronic Structure, Electrical, Magnetic and Optical Properties
DOI http://dx.doi.org/10.1209/0295-5075/81/57003
Published online 04 February 2008
EPL, 81 (2008) 57003
DOI: 10.1209/0295-5075/81/57003

Exact relationship between the entanglement entropies of XY and quantum Ising chains

F. Iglói1, 2 and R. Juhász1

1  Research Institute for Solid State Physics and Optics - P.O. Box 49, H-1525 Budapest, Hungary
2  Institute of Theoretical Physics, Szeged University - H-6720 Szeged, Hungary


received 24 September 2007; accepted in final form 4 January 2008; published March 2008
published online 4 February 2008

Abstract
We consider two prototypical quantum models, the spin-1/2 XY chain and the quantum Ising chain and study their entanglement entropy, $S(\ell,L)$, of blocks of $\ell $ spins in homogeneous or inhomogeneous systems of length L. By using two different approaches, free-fermion techniques and perturbational expansion, an exact relationship between the entropies is revealed. Using this relation we translate known results between the two models and obtain, among others, the additive constant of the entropy of the critical homogeneous quantum Ising chain and the effective central charge of the random XY chain.

PACS
75.10.Jm - Quantized spin models.
75.10.Pq - Spin chain models.
03.65.Ud - Entanglement and quantum nonlocality (e.g. EPR paradox, Bell's inequalities, GHZ states, etc.).

© EPLA 2008