Entanglement entropy of two disjoint blocks in XY chains

Journal of Statistical Mechanics: Theory and Experiment

Volumn 2010, Issue 4, 2010, Pages

  Fagotti, Maurizio ^a   Calabrese, Pasquale ^a  

^a INFN SEZIONE DI PISA   (Italy)

Author keywords

Conformal field theory (theory); Entanglement in extended quantum systems (theory); Ladders and planes (theory); Spin chains

Indexed keywords

EID: 77951675681     PISSN: 17425468     EISSN: 17425468     Source Type: Journal    
DOI: 10.1088/1742-5468/2010/04/P04016     Document Type: Article

References (78)

1. Amico L, Fazio R, Osterloh A and Vedral V 2008 Entanglement in many-body systems Rev. Mod. Phys. 80 517 (Pubitemid 351697445)
2. Eisert J, Cramer M and Plenio M B 2010 Area laws for the entanglement entropy-a review Rev. Mod. Phys. 82 277
3. Calabrese P, Cardy J and Doyon B (ed) 2009 Entanglement entropy in extended systems J. Phys. A: Math. Theor. 42 500301
4. Calabrese P and Lefevre A 2008 Entanglement spectrum in one-dimensional systems Phys. Rev. A 78 032329
5. Schuch N, Wolf M M, Verstraete F and Cirac J I 2008 Entropy scaling and simulability by matrix product states Phys. Rev. Lett. 100 030504 (Pubitemid 351161830)
6. Perez-Garcia D, Verstraete F, Wolf M M and Cirac J I 2007 Matrix product state representations Quantum Inf. Comput. 7 401
7. Tagliacozzo L, de Oliveira T R, Iblisdir S and Latorre J I 2008 Scaling of entanglement support for matrix product states Phys. Rev. B 78 024410
8. Pollmann F, Mukerjee S, Turner A M and Moore J E 2009 Theory of finite-entanglement scaling at one-dimensional quantum critical points Phys. Rev. Lett. 102 255701
9. Verstraete F and Cirac J I 2009 Renormalization and tensor product states in spin chains and lattices J. Phys. A: Math. Theor. 42 504004
10. Holzhey C, Larsen F and Wilczek F 1994 Geometric and renormalized entropy in conformal field theory Nucl. Phys. B 424 443 (Pubitemid 124002743)
11. Calabrese P and Cardy J 2004 Entanglement entropy and quantum field theory J. Stat. Mech. P06002
12. Calabrese P and Cardy J 2009 Entanglement entropy and conformal field theory J. Phys. A: Math. Theor. 42 504005
13. Casini H, Fosco C D and Huerta M 2005 Entanglement and alpha entropies for a massive Dirac field in two dimensions J. Stat. Mech. P05007
14. Casini H and Huerta M 2009 Remarks on the entanglement entropy for disconnected regions J. High Energy Phys. JHEP03(2009)048
15. Casini H and Huerta M 2009 Reduced density matrix and internal dynamics for multicomponent regions Class. Quantum Grav. 26 185005
16. Facchi P, Florio G, Invernizzi C and Pascazio S 2008 Entanglement of two blocks of spins in the critical Ising model Phys. Rev. A 78 052302
17. Klich I and Levitov L 2009 Quantum noise as an entanglement meter Phys. Rev. Lett. 102 100502
18. Caraglio M and Gliozzi F 2008 Entanglement entropy and twist fields J. High Energy Phys. JHEP11(2008)076
19. Furukawa S, Pasquier V and Shiraishi J 2009 Mutual information and compactification radius in a c = 1 critical phase in one dimension Phys. Rev. Lett. 102 170602
20. Calabrese P, Cardy J and Tonni E 2009 Entanglement entropy of two disjoint intervals in conformal field theory J. Stat. Mech. P11001
21. Alba V, Tagliacozzo L and Calabrese P 2010 Entanglement entropy of two disjoint blocks in critical Ising models Phys. Rev. B 81 060411
22. Dixon L J, Friedan D, Martinec E J and Hshenker S 1987 The conformal field theory of orbifolds Nucl. Phys. B 282 13
23. Zamolodchicov Al B 1987 Conformal scalar field on the hyperelliptic curve and critical Ashkin-Teller multipoint correlation functions Nucl. Phys. B 285 481
24. Knizhnik V G 1987 Analytic fields on Riemann surfaces. II Commun. Math. Phys. 112 567
25. N symmetry Int. J. Mod. Phys. A 2 165
26. Wichterich H, Molina-Vilaplana J and Bose S 2009 Scale invariant entanglement at quantum phase transitions Phys. Rev. A 80 010304(R)
27. Marcovitch S, Retzker A, Plenio M B and Reznik B 2009 Critical and noncritical long range entanglement in the Klein-Gordon field Phys. Rev. A 80 012325
28. Wichterich H, Vidal J and Bose S 2010 Universality of the negativity in the Lipkin-Meshkov-Glick model Phys. Rev. A 81 032311
29. Igloi F and Peschel I 2010 On reduced density matrices for disjoint subsystems Europhys. Lett. 89 40001
30. Alba V, Fagotti M and Calabrese P 2009 Entanglement entropy of excited states J. Stat. Mech. P10020
31. 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
32. Kitanine N, Maillet J M and Terras V 2000 Correlation functions of the XXZ Heisenberg spin-1/2 chain in a magnetic field Nucl. Phys. B 567 554
33. Sato J and Shiroishi M 2007 Density matrix elements and entanglement entropy for the spin-1/2 XXZ chain at Δ = 1/2 J. Phys. A: Math. Theor. 40 8739
34. Damerau J, Göhmann F, Hasenclever N P and Klümper A 2007 Density matrices for finite segments of Heisenberg chains of arbitrary length J. Phys. A: Math. Theor. 40 4439
35. Boos H E, Damerau J, Göhmann F, Klümper A, Suzuki J and Weisse A 2008 Short-distance thermal correlations in the XXZ chain J. Stat. Mech. P08010
36. Trippe C, Göhmann F and Klümper A 2009 Short-distance thermal correlations in the massive XXZ chain Eur. Phys. J. B 73 253
37. Sato J, Shiroishi M and Takahashi M 2006 Exact evaluation of density matrix elements for the Heisenberg chain J. Stat. Mech. P12017
38. Katsura H and Maruyama I 2009 Derivation of matrix product ansatz for the Heisenberg chain from algebraic Bethe ansatz arXiv:0911.4215
39. Vidal G, Latorre J I, Rico E and Kitaev A 2003 Entanglement in quantum critical phenomena Phys. Rev. Lett. 90 227902
40. Latorre J I, Rico E and Vidal G 2004 Ground state entanglement in quantum spin chains Quantum Inform. Comput. 4 048 (Pubitemid 38411039)
41. Latorre J I and Riera A 2009 A short review on entanglement in quantum spin systems J. Phys. A: Math. Theor. 42 504002
42. Peschel I and Eisler V 2009 Reduced density matrices and entanglement entropy in free lattice models J. Phys. A: Math. Theor. 42 504003
43. Jin B-Q and Korepin V E 2004 Quantum spin chain, Toeplitz determinants and Fisher-Hartwig conjecture J. Stat. Phys. 116 79
44. Its A R, Jin B-Q and Korepin V E 2005 Entanglement in XY spin chain J. Phys. A: Math. Gen. 38 2975
45. Franchini F, Its A R and Korepin V E 2008 Renyi entropy of the XY spin chain J. Phys. A: Math. Theor. 41 025302
46. Calabrese P, Campostrini M, Essler F and Nienhuis B 2010 Parity effects in the scaling of block entanglement in gapless spin chains Phys. Rev. Lett. 104 095701
47. Ikramov Kh D and Fasbender H 2009 On the product of two skew-Hamiltonians or two skew-symmetric matrices J. Math. Sci. 157 697
48. Laflorencie N, Sorensen E S, Chang M-S and Affleck I 2006 Boundary effects in the critical scaling of entanglement entropy in 1D systems Phys. Rev. Lett. 96 100603
49. Sorensen E S, Laflorencie N and Affleck I 2009 Entanglement entropy in quantum impurity systems and systems with boundaries J. Phys. A: Math. Theor. 42 504009
50. Zhou H-Q, Barthel T, Fjaerestad J O and Schollwoeck U 2006 Entanglement and boundary critical phenomena Phys. Rev. A 74 050305
51. De Chiara G, Montangero S, Calabrese P and Fazio R 2006 Entanglement entropy dynamics in Heisenberg chains J. Stat. Mech. P03001
52. Legeza O, Solyom J, Tincani L and Noack R M 2007 Entropic analysis of quantum phase transitions from uniform to spatially inhomogeneous phases Phys. Rev. Lett. 99 087203 (Pubitemid 47331094)
53. Laeuchli A and Kollath C 2008 Spreading of correlations and entanglement after a quench in the Bose-Hubbard model J. Stat. Mech. P05018
54. Roux G, Capponi S, Lecheminant P and Azaria P 2009 Spin 3/2 fermions with attractive interactions in a one-dimensional optical lattice: phase diagrams, entanglement entropy, and the effect of the trap Eur. Phys. J. B 68 293
55. Nienhuis B, Campostrini M and Calabrese P 2009 Entanglement, combinatorics and finite-size effects in spin-chains J. Stat. Mech. P02063
56. Gliozzi F and Tagliacozzo L 2010 Entanglement entropy and the complex plane of replicas J. Stat. Mech. P01002
57. Cirac I J and Sierra G 2009 Infinite matrix product states, conformal field theory and the Haldane-Shastry model arXiv:0911.3029
58. Hastings M B, Gonzalez I, Kallin A B and Melko R G 2010 Measuring Renyi entanglement entropy with quantum Monte Carlo arXiv:1001.2335
59. Xavier J C 2010 Entanglement entropy, conformal invariance and the critical behavior of the anisotropic spin-S Heisenberg chains: a DMRG study arXiv:1002.0531
60. Song H F, Rachel S and Le Hur K 2010 General relation between entanglement and fluctuations in one dimension arXiv:1002.0825
61. Alcaraz F C and Rittenberg V 2010 Shared information in stationary states at criticality J. Stat. Mech. P03024
62. Kallin A B, Gonzlez I, Hastings M B and Melko R 2009 Valence bond and von Neumann entanglement entropy in Heisenberg ladders Phys. Rev. Lett. 103 117203
63. Cardy J and Calabrese P 2010 Unusual corrections to scaling in entanglement entropy arXiv:1002.4353
64. Peschel I 2004 On the entanglement entropy for a XY spin chain J. Stat. Mech. P12005
65. Igloi F and Juhasz R 2008 Exact relationship between the entanglement entropies of XY and quantum Ising chains Europhys. Lett. 81 57003
66. 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
67. Castro-Alvaredo O A and Doyon B 2008 Bi-partite entanglement entropy in integrable models with backscattering J. Phys. A: Math. Theor. 41 275203
68. 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
69. Calabrese P and Cardy J 2005 Evolution of Entanglement entropy in one dimensional systems J. Stat. Mech. P04010 (Pubitemid 40669590)
70. Fagotti M and Calabrese P 2008 Evolution of entanglement entropy following a quantum quench: analytic results for the XY chain in a transverse magnetic field Phys. Rev. A 78 010306
71. Sotiriadis S and Cardy J 2008 Inhomogeneous quantum quenches J. Stat. Mech. P11003
72. Eisler V and Peschel I 2007 Evolution of entanglement after a local quench J. Stat. Mech. P06005
73. Eisler V, Karevski D, Platini T and Peschel I 2008 Entanglement evolution after connecting finite to infinite quantum chains J. Stat. Mech. P01023
74. Refael G and Moore J E 2004 Entanglement entropy of random quantum critical points in one dimension Phys. Rev. Lett. 93 260602 (Pubitemid 40213716)
75. Refael G and Moore J E 2005 Scaling of entanglement entropy in the random singlet phase Phys. Rev. B 72 140408(R)
76. Santachiara R 2006 Increasing of entanglement entropy from pure to random quantum critical chains J. Stat. Mech. L06002 (Pubitemid 44060210)
77. Refael G and Moore J E 2009 Criticality and entanglement in random quantum systems J. Phys. A: Math. Theor. 42 504010
78. Palmer J 1989 Pfaffian bundles and the Ising model Commun. Math. Phys. 120 547