Permutation operators, entanglement entropy, and the XXZ spin chain in the limit Δ → -1+

Journal of Statistical Mechanics: Theory and Experiment

Volumn 2011, Issue 2, 2011, Pages

  Castro Alvaredo, Olalla A ^a   Doyon, Benjamin ^b  

^a CITY UNIVERSITY   (United Kingdom)

^b KING'S COLLEGE LONDON   (United Kingdom)

Author keywords

correlation functions; entanglement in extended quantum systems (theory); integrable spin chains (vertex models)

Indexed keywords

EID: 79952730898     PISSN: 17425468     EISSN: 17425468     Source Type: Journal    
DOI: 10.1088/1742-5468/2011/02/P02001     Document Type: Article

References (45)

1. Bennet C H, Bernstein H J, Popescu S and Schumacher B 1996 Concentrating partial entanglement by local operations Phys. Rev. A 53 2046
2. Rényi A 1970 Probability Theory (Amsterdam: North-Holland)
3. Weston R A 2006 The entanglement entropy of solvable lattice models J. Stat. Mech. L03002
4. Ercolessi E, Evangelisti S and Ravanini F 2010 Exact entanglement entropy of the XYZ model and its sine-Gordon limit Phys. Lett. A 374 2101
5. Ercolessi E, Evangelisti S, Franchini F and Ravanini F 2010 Unusual singular behavior of the entanglement entropy in one dimension arXiv:1008.3892
6. Vidal G, Latorre J I, Rico E and Kitaev A 2003 Entanglement in quantum critical phenomena Phys. Rev. Lett. 90 227902
7. Latorre J I, Rico E and Vidal G 2004 Ground state entanglement in quantum spin chains Quant. Inf. Comput. 4 48
8. Latorre J I, Lutken C A, Rico E and Vidal G 2005 Fine-grained entanglement loss along renormalization group flows Phys. Rev. A 71 034301
9. Jin B-Q and Korepin V 2004 Quantum spin chain, Toeplitz determinants and Fisher-Hartwig conjecture J. Stat. Phys. 116 79
10. Lambert N, Emary C and Brandes T 2004 Entanglement and the phase transition in single-mode superradiance Phys. Rev. Lett. 92 073602
11. Keating J P and Mezzadri F 2005 Entanglement in quantum spin chains, symmetry classes of random matrices, and conformal field theory Phys. Rev. Lett. 94 050501
12. Callan C G Jr and Wilczek F 1994 On geometric entropy Phys. Lett. B 333 55
13. Holzhey C, Larsen F and Wilczek F 1994 Geometric and renormalized entropy in conformal field theory Nucl. Phys. B 424 443
14. Calabrese P and Cardy J L 2004 Entanglement entropy and quantum field theory J. Stat. Mech. P06002
15. Calabrese P and Cardy J L 2005 Evolution of entanglement entropy in one-dimensional Systems J. Stat. Mech. P04010
16. Caraglio M and Gliozzi F 2008 Entanglement entropy and twist fields J. High Energy Phys. JHEP11(2008)076
17. Casini H and Huerta M 2009 Reduced density matrix and internal dynamics for multicomponent regions Class. Quantum Grav. 26 185005
18. Casini H and Huerta M 2009 Remarks on the entanglement entropy for disconnected regions J. High Energy Phys. JHEP03(2009)048
19. Calabrese P, Cardy J and Tonni E 2009 Entanglement entropy of two disjoint intervals in conformal field theory J. Stat. Mech. P11001
20. Calabrese P, Cardy J and Tonni E 2011 Entanglement entropy of two disjoint intervals in conformal field theory II J. Stat. Mech. P01021
21. Fagotti M and Calabrese P 2010 Entanglement entropy of two disjoint blocks in XY chains J. Stat. Mech. P04016
22. Alba V, Tagliacozzo L and Calabrese P 2010 Entanglement entropy of two disjoint blocks in critical Ising models Phys. Rev. B 81 060411(R)
23. Cardy J L, Castro-Alvaredo O A and Doyon B 2008 Form factors of branch-point twist fields in quantum integrable models and entanglement entropy J. Stat. Phys. 130 129
24. Castro-Alvaredo O A and Doyon B 2008 Bi-partite entanglement entropy in integrable models with backscattering J. Phys. A: Math. Theor. 41 275203
25. Doyon B 2009 Bi-partite entanglement entropy in massive two-dimensional quantum field theory Phys. Rev. Lett. 102 031602
26. Castro-Alvaredo O A and Doyon B 2009 Bi-partite entanglement entropy in massive QFT with a boundary: the Ising model J. Stat. Phys. 134 105
27. Castro-Alvaredo O A and Doyon B 2009 Bi-partite entanglement entropy in massive 1 + 1-dimensional quantum field theories J. Phys. A: Math. Theor. 42 504006
28. Banchi L, Colomo F and Verruchi P 2009 When finite-size corrections vanish: the S = 1/2 XXZ model and the Razumov-Stroganov state Phys. Rev. A 80 022341
29. Castro-Alvaredo O and Doyon B Entanglement entropy of the XXZ chain at Δ = - 1, in preparation
30. Faddeev L D 1996 How Algebraic Bethe ansatz works for integrable models Presented at Les Houches 1995 pp149-219
31. Maillet J-M and Terras V 2000 On the quantum inverse scattering problem Nucl. Phys. B 575 627
32. Faddeev L D, Sklyanin E K and Takhtajan L A 1980 The quantum inverse problem method. 1 Theor. Math. Phys. 40 688
33. Faddeev L D, Sklyanin E and Takhtajan L 1979 Quantum inverse scattering method I Theor. Math. Phys. 40 194
34. Korepin V, Bogoliugov N and Izergin A 1993 Quantum inverse scattering method and correlation functions (Cambridge: Cambridge University Press)
35. Kitanine N, Maillet J-M and Terras V 1999 Form Factors of the XXZ Heisenberg spin-1/2 finite chain Nucl. Phys. B 554 647
36. Kitanine N, Maillet J-M and Terras V 2000 Correlation functions of the XXZ Heisemberg spin-1/2 chain in a magnetic field Nucl. Phys. B 567 554
37. Jimbo M and Miwa T 1996 Quantum KZ equation with Q = 1 and correlation functions of the XXZ model in the gapless regime J. Phys. A: Math. Gen. 29 2923
38. Jimbo M and Miwa T 1995 Algebraic Analysis of Solvable Lattice Models (Providence, RI: American Mathematical Society)
39. Jimbo M, Miki K, Miwa T and Nakayashiki A 1992 Correlation functions of the XXZ model for Δ < - 1 Phys. Lett. A 168 256
40. Kitanine N, Maillet J M, Slavnov N A and Terras V 2005 On the spin-spin correlation functions of the XXZ spin-1/2 infinite chain J. Phys. A: Math. Gen. 38 7441
41. Kato G, Shiroishi M, Takahashi M and Sakai K 2003 Next nearest-neighbor correlation functions of the spin-1/2 XXZ chain at critical region J. Phys. A: Math. Gen. 36 L337
42. Kato G, Shiroishi M, Takahashi M and Sakai K 2004 Third-neighbor and other four-point correlation functions of spin-1/2 XXZ chain J. Phys. A: Math. Gen. 37 5097
43. Kitanine N, Maillet J-M, Slavnov N A and Terras V 2002 Correlation functions of the XXZ spin-1/2 Heisenberg chain at the free fermion point from their multiple integral representations Nucl. Phys. B 642 433
44. Lukyanov S L and Terras V 2003 Long-distance asymptotics of spin-spin correlation functions for the XXZ spin chain Nucl. Phys. B 654 323
45. Kitanine N, Kozlowski K K, Maillet J M, Slavnov N A and Terras V 2009 Algebraic Bethe ansatz approach to the asymptotic behavior of correlation functions J. Stat. Mech. P04003