Entanglement entropy in quantum spin chains with finite range interaction

Communications in Mathematical Physics

Volumn 284, Issue 1, 2008, Pages 117-185

  Its, A R ^a   Mezzadri, F ^b   Mo, M Y ^b  

^a INDIANA UNIVERSITY   (United States)

^b UNIVERSITY OF BRISTOL   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 53349177456     PISSN: 00103616     EISSN: 14320916     Source Type: Journal    
DOI: 10.1007/s00220-008-0566-6     Document Type: Article

References (25)

1. Belokolos E.D., Bobenko A.I., Enolskii V.Z., Its A.R., Matveev V.B.: Algebro-geometric approach to nonlinear integrable equations. Springer series in nonlinear dynamics. Springer-Verlag, Berlin-Heidelberg-New York (1995)
2. C.H. Bennett H.J. Bernstein S. Popescu B. Schumacher 1996 Concentrating partial entanglement by local operations Phys. Rev. A 53 2046 2052
3. Calabrese, P., Cardy, J.: Entanglement entropy and quantum field theory. J. Stat. Mech. The. Exp., P06002 (2004)
4. Calabrese, P., Cardy, J.: Evolution of entanglement entropy in one-dimensional systems. J. Stat. Mech. The. Exp., P04010 (2005)
5. P.A. Deift 1999 Integrable operators Amer. Math. Soc. Transl. (2) 189 69 84
6. Farkas H.M., Kra I.: Riemann surfaces. Graduate Texts in Mathematics, 71. Springer-Verlag, New York-Berlin (1980)
7. Rauch H.E., Farkas H.M.: Theta functions with applications to Riemann surfaces. The Williams and Wilkins Co.,, Baltimore, MD (1974)
8. A.S. Fokas Zhou. Xin 1992 On the solvability of Painlev II and IV Commun. Math. Phys. 144 3 601 622
9. J. Harnad A.R. Its 2002 Integrable Fredholm operators and dual isomonodromic deformations Comm. Math. Phys. 226 497 530
10. C. Holzhey F. Larsen F. Wilczek 1994 Geometric and renormalized entropy in conformal field theory Nucl. Phys. B 424 443 467
11. A.R. Its A.G. Izergin V.E. Korepin N.A. Slavnov 1990 Differential equations for quantum correlation functions Proceedings of the Conference on Yang-Baxter Equations, Conformal Invariance and Integrability in Statistical Mechanics and Field Theory. Int. J. Mod. Phys. B 4 1003 1037
12. A.R. Its B.Q. Jin V.E. Korepin 2005 Entanglement in the XY spin chain J. Phys. A 38 2975 2990
13. Its, A.R., Jin, B.Q., Korepin, V.E.: Entropy of XY Spin Chain and Block Toeplitz Determinants. In: Filds Inst. Commun. Universality and Renormalization, I. Bender, D. Kneimer (eds.), Vol. 50, Providence, RI: Amer. Math. Soc., 2007, P. 151
14. B.Q. Jin V.E. Korepin 2004 Entanglement, Toeplitz determinants and Fisher-Hartwig conjecture J. Stat. Phys. 116 79 95
15. V.E. Korepin 2004 Universality of entropy scaling in 1D gap-less models Phys. Rev. Lett. 92 096402
16. Griffiths P., Harris J.: Principles of Algebraic Geometry. Wiley Interscience, New York (1978)
17. E. Lieb T. Schultz D. Mattis 1961 Two soluble models of an antiferromagnetic chain Ann. Phys. 16 407 466
18. J.P. Keating F. Mezzadri 2004 Random matrix theory and entanglement in quantum spin chains Commun. Math. Phys. 242 543 579
19. J.P. Keating F. Mezzadri 2005 Entanglement in quantum spin chains, symmetry classes of random matrices, and conformal field theory Phys. Rev. Lett. 94 050501
20. A. Osterloh L. Amico G. Falci R. Fazio 2002 Scaling of entanglement close to a quantum phase transition Nature 416 608 610
21. Peschel, I.: On the entanglement entropy for an XY spin chain. J. Stat. Mech. The. Exp., P12005 (2004)
22. T.J. Osborne M.A. Nielsen 2002 Entanglement in a simple quantum phase transition Phys. Rev. A 66 032110
23. G. Vidal J.I. Latorre E. Rico A. Kitaev 2003 Entanglement in quantum critical phenomena Phys. Rev. Lett. 90 227902
24. H. Widom 1974 Asymptotic behavior of block Toeplitz matrices and determinants Adv. Math. 13 284 322
25. H. Widom 1975 On the limit of block Toeplitz determinants Proc. Amer. Math. Soc. 50 167 173