Correlation functions of the open XXZ chain: I

Journal of Statistical Mechanics: Theory and Experiment

Volumn , Issue 10, 2007, Pages

  Kitanine, N ^a   Kozlowski, K K ^b   Maillet, J M ^b   Niccoli, G ^a   Slavnov, N A ^c   Terras, V ^b,d  

^a Université de Cergy Pontoise   (France)

^b UNIVERSITÉ DE LYON   (France)

^c STEKLOV MATHEMATICAL INSTITUTE   (Russian Federation)

^d CENTRE DE CALCUL DE L INSTITUT NATIONAL DE PHYSIQUE NUCLEAIRE ET DE PHYSIQUE DES PARTICULES   (France)

Author keywords

Boundary solvable models; Correlation functions; Integrable spin chains (vertex models); Quantum integrability (Bethe ansatz)

Indexed keywords

EID: 35948930661     PISSN: 17425468     EISSN: 17425468     Source Type: Journal    
DOI: 10.1088/1742-5468/2007/10/P10009     Document Type: Article

References (115)

1. Heisenberg W 1928 Zur theorie der ferromagnetismus Z. Phys. 49 619
2. Fujimoto S 2003 Low-temperature anomaly at the edge of the Heisenberg spin chains: a boundary conformal field theory approach Preprint (unpublished) cond-mat/0308046
3. Fujimoto S and Eggert S 2004 Boundary susceptibility in the spin-1/2 chain: Curie like behavior without magnetic impurities Phys. Rev. Lett. 92 037206
4. Furusaki A and Hikihara T 2004 Boundary contributions to specific heat and susceptibility in the spin-1/2 XXZ chain Phys. Rev. B 69 094429
5. Hikihara T and Furusaki A 2004 Correlation amplitudes for the spin-1/2 XXZ chain in a magnetic field Phys. Rev. B 69 064427
6. Bortz M and Sirker J 2005 Boundary susceptibility in the open XXZ-chain J. Phys. A: Math. Gen. 38 5957
7. Göhmann F, Bortz M and Frahm H 2005 Surface free energy for systems with integrable boundary conditions J. Phys. A: Math. Gen. 38 10879
8. Sirker J and Bortz M 2006 Quantum versus classical behavior in the boundary susceptibility of the ferromagnetic Heisenberg chain Phys. Rev. B 73 014424
9. Sirker J and Bortz M 2006 The open XXZ-chain: bosonization, the Bethe ansatz and logarithmic corrections J. Stat. Mech. P01007
10. 3+δ and other doped quasi-one-dimensional antiferromagnets Phys. Rev. Lett. 98 137205
11. 3 studied by muon spin rotation J. Magn. Magn. Mater. 272 979
12. Vidal G, Latorre J I, Rico E and Kitaev A 2003 Entanglement in quantum critical phenomena Phys. Rev. Lett. 90 227902
13. Calabrese P and Cardy J 2004 Entanglement entropy and quantum field theory J. Stat. Mech. P06002
14. Calabrese P and Cardy J 2005 Evolution of entanglement entropy in one-dimensional systems J. Stat. Mech. P04010
15. Osterloh A, Amico L, Falci G and Fazio R 2002 Scaling of entanglement close to a quantum phase transition Nature 416 608
16. Osborne T J and Nielsen M A 2002 Entanglement in a simple quantum phase transition Phys. Rev. A 66 032110
17. Refael G and Moore J E 2004 Entanglement entropy of random quantum critical points in one dimension Phys. Rev. Lett. 93 260602
18. Korepin V E 2004 Universality of entropy scaling in one dimensional gapless models Phys. Rev. Lett. 92 096402
19. Laflorencie N 2005 Scaling of entanglement entropy in the random singlet phase Phys. Rev. B 72 140408
20. Laflorencie N, Sørensen 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
21. Egger R and Grabert H 1995 Friedel oscillations for interacting fermions in one dimension Phys. Rev. Lett. 75 3505
22. Fabrizio M and Gogolin A 1995 Interacting one dimensional electron gas with open boundaries Phys. Rev. B 51 17827
23. Bedürftig G, Brendel B, Frahm H and Noack R 1998 Friedel oscillations in the open Hubbard chain Phys. Rev. B 58 10225
24. Bloch F 1936 On the magnetic scattering of neutrons Phys. Rev. 50 259
25. Schwinger J S 1937 On the magnetic scattering of neutrons Phys. Rev. 51 544
26. Halpern O and Johnson M H 1938 On the magnetic scattering of neutrons Phys. Rev. 55 898
27. Van Hove L 1954 Correlations in space and time and Born approximation scattering in systems of interacting particles Phys. Rev. 95 249
28. Van Hove L 1954 Time dependent correlations between spins and neutron scattering in ferromagnatic crystals Phys. Rev. 95 1374
29. Marshall W and Lovesey S W 1971 Theory of Thermal Neutron Scattering (Oxford: Academic)
30. Balescu R 1975 Equilibrium and Nonequilibrium Statistical Mechanics (New York: Wiley)
31. Bethe H 1931 Zur theorie der metalle I. eigenwerte und eigenfunktionen atomkete Z. Phys. 71 205
32. Hulthen L 1938 ber das austauschproblem eines kristalls Ark. Mat. Astron. Fys. 26 1
33. Orbach R 1958 Linear antiferromagnetic chain with anisotropic coupling Phys. Rev. 112 309
34. Walker L R 1959 Antiferromagnetic linear chain Phys. Rev. 116 1089
35. Yang C N and Yang C P 1966 One-dimensional chain of anisotropic spin-spin interactions. I. Proof of Bethe's hypothesis for ground state in a finite system Phys. Rev. 150 321
36. Yang C N and Yang C P 1966 One-dimensional chain of anisotropic spin-spin interactions. II. Properties of the ground state energy per lattice site for an infinite system Phys. Rev. 150 327
37. Baxter R J 1982 Exactly Solved Models in Statistical Mechanics (London: Academic)
38. Gaudin M 1983 La Fonction d'onde de Bethe (Paris: Masson)
39. Lieb E H and Mattis D C 1966 Mathematical Physics in One Dimension (New-York: Academic)
40. Thacker H B 1981 Exact integrability in quantum field theory and statistical systems Rev. Mod. Phys. 53 253
41. Korepin V E, Bogoliubov N M and Izergin A G 1993 Quantum Inverse Scattering Method and Correlation Functions (Cambridge: Cambridge University Press)
42. Jimbo M and Miwa T 1995 Algebraic Analysis of Solvable Lattice Models (Washington, DC: AMS)
43. Faddeev L D, Sklyanin E K and Takhtajan L A 1980 Quantum inverse problem method I Theor. Math. Phys. 40 688
44. Takhtajan L A and Faddeev L D 1979 The Quantum method of the inverse problem and the Heisenberg XYZ model Russ. Math. Surveys 34 11
45. Onsager L 1944 Cristal statistics I. A two-dimensional model with an order-disorder transition Phys. Rev. 65 117
46. Kaufmann B 1949 Crystal statistics II. Partition function evaluated by spinor analysis Phys. Rev. 76 1232
47. Kaufmann B and Onsager L 1949 Cristal statistics III. Short range order in a binary Ising lattice Phys. Rev. 76 1244
48. Yang C N 1952 The spontaneous magnetization of a two-dimensional Ising model Phys. Rev. 85 808
49. Lieb E, Schultz T and Mattis D 1961 Two soluble models of an antiferromagnetic chain Ann. Phys. 16 407
50. McCoy B 1968 Spin correlation functions of the XY model Phys. Rev. 173 531
51. Wu T T, McCoy B M, Tracy C A and Barouch E 1976 The spin-spin correlation function of the two-dimensional Ising model: exact results in the scaling region Phys. Rev. B 13 316
52. McCoy B M, Tracy C A and Wu T T 1977 Two-dimensional Ising model as an exactly soluble relativistic quantum field theory: explicit formulas for the n-point functions Phys. Rev. Lett. 38 793
53. Sato M, Miwa T and Jimbo M 1978 Holonomic quantum fields Publ. Res. Inst. Math. Sci. 14 223
54. Sato M, Miwa T and Jimbo M 1979 Publ. Res. Inst. Math. Sci. 15 201 577
55. Sato M, Miwa T and Jimbo M 1979 Publ. Res. Inst. Math. Sci. 15 201 871
56. Sato M, Miwa T and Jimbo M 1980 Publ. Res. Inst. Math. Sci. 16 531
57. Izergin A G and Korepin V E 1984 The quantum inverse scattering method approach to correlation functions Commun. Math. Phys. 94 67
58. Izergin A G and Korepin V E 1985 Correlation functions for the Heisenberg XXZ-antiferromagnet Commun. Math. Phys. 99 271
59. Jimbo M, Miki K, Miwa T and Nakayashiki A 1992 Correlation functions of the XXZ model for Δ<-1 Phys. Lett. A 168 256
60. 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
61. Maillet J M and Sanchez de Santos J 2000 Drinfeld twists and algebraic Bethe ansatz Am. Math. Soc. Transl. 201 137
62. 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
63. 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
64. Maillet J M and Terras V 2000 On the quantum inverse scattering problem Nucl. Phys. B 575 627
65. Kitanine N, Maillet J M, Slavnov N A and Terras V 2002 Spin-spin correlation functions of the XXZ-1/2 Heisenberg chain in a magnetic field Nucl. Phys. B 641 487
66. 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
67. Kitanine N, Maillet J M, Slavnov N A and Terras V 2002 Emptiness formation probability of the XXZ spin-1/2 Heisenberg chain at Delta = 1/2 J. Phys. A: Math. Gen. 35 L385
68. Kitanine N, Maillet J M, Slavnov N A and Terras V 2002 Large distance asymptotic behaviour of the emptiness formation probability of the XXZ spin-1/2 Heisenberg chain J. Phys. A: Math. Gen. 35 L753
69. Kitanine N, Maillet J M, Slavnov N A and Terras V 2005 Master equation for spin-spin correlation functions of the XXZ chain Nucl. Phys. B 712 600
70. Kitanine N, Maillet J M, Slavnov N A and Terras V 2005 Dynamical correlation functions of the XXZ spin-1/2 chain Nucl. Phys. B 729 558
71. 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
72. Göhmann F, Klümper A and Seel A 2004 Integral representations for correlation functions of the XXZ chain at finite temperature J. Phys. A: Math. Gen. 37 7625
73. Göhmann F, Klümper A and Seel A 2005 Integral representation of the density matrix of the XXZ chain at finite temperatures J. Phys. A: Math. Gen. 38 1833
74. Göhmann F, Klümper A and Seel A 2005 Emptiness formation probability at finite temperature for the isotropic Heisenberg chain Physica B 359 807
75. Göhmann F, Hasenclever N P and Seel A 2005 The finite temperature density matrix and two-point correlations in the antiferromagnetic XXZ chain J. Stat. Mech. P10015
76. Kitanine N, Maillet J M, Slavnov N A and Terras V 2005 Exact results for the sigma-z two-point function of the XXZ chain at Delta = 1/2 J. Stat. Mech. L09002
77. Kitanine N, Maillet J M, Slavnov N A and Terras V 2006 On the algebraic Bethe ansatz approach to the correlation functions of the XXZ spin-1/2 Heisenberg chain Recent Progress in Solvable lattice Models, RIMS Sciences Project Research 2004 on Method of Algebraic Analysis in Integrable Systems (RIMS, Kyoto, Kokyuroku) vol 1480 p14 [hep-th/0505006]
78. Caux J-S and Maillet J M 2005 Computation of dynamical correlation functions of Heisenberg chains in a field Phys. Rev. Lett. 95 077201
79. Caux J-S, Hagemans R and Maillet J M 2005 Computation of dynamical correlation functions of Heisenberg chains: the gapless anysotropic regime J. Stat. Mech. P09003
80. Pereira R G, Sirker J, Caux J-S, Hagemans R, Maillet J M, White S R and Affleck I 2006 Dynamical spin structure factor for the anisotropic spin-1/2 Heisenberg chain Phys. Rev. Lett. 96 257202
81. Boos H, Jimbo M, Miwa T, Smirnov F and Takeyama Y 2006 Reduced q-KZ equation and correlation functions of the XXZ model Commun. Math. Phys. 261 245
82. Boos H, Jimbo M, Miwa T, Smirnov F and Takeyama Y 2006 Density matrix of a finite sub-chain of the Heisenberg anti-ferromagnet Lett. Math. Phys. 75 201
83. Boos H, Jimbo M, Miwa T, Smirnov F and Takeyama Y 2006 Algebraic representation of correlation functions in integrable spin chains Ann. Henri Poincare 7 1395
84. Boos H, Jimbo M, Miwa T, Smirnov F and Takeyama Y 2007 Hidden Grassmann structure in the XXZ model Commun. Math. Phys. 272 263
85. Jimbo M, Kedem R, Kojima T, Konno H and Miwa T 1995 XXZ chain with a boundary Nucl. Phys. B 441 437
86. Jimbo M, Kedem R, Konno H, Miwa T and Weston R 1995 Difference equations in spin chains with a boundary Nucl. Phys. B 448 429
87. Affleck I 1988 Fields, Strings and Critical Phenomena (Proc. Les Houches Summer School, Session XLIX) ed E Brezin and J Zinn-Justin (Amsterdam: Elsevier) p563
88. Affleck I and Ludwig A W W 1991 The Kondo effect, conformal field theory and fusion rules Nucl. Phys. B 352 849
89. Eggert S and Affleck I 1992 Magnetic impurities in half-integer-spin Heisenberg antiferromagnetic chains Phys. Rev. B 46 10866
90. Eggert S and Affleck I 1995 Impurities in S = 1/2 Heisenberg antiferromagnetic chains: consequences for neutron scattering and knight shift Phys. Rev. Lett. 75 934
91. Wessel S and Haas S 2000 Excitation spectra and thermodynamic response of segmented Heisenberg spin chains Phys. Rev. B 61 15262
92. Bilstein U and Wehefritz B 1999 The XX-model with boundaries: Part I. Diagonalization of the finite chain J. Phys. A: Math. Gen. 32 191
93. Bilstein U 2000 The XX model with boundaries: II. Finite-size scaling and partition functions J. Phys. A: Math. Gen. 33 4437
94. Bilstein U 2000 The XX-model with boundaries: III. Magnetization profiles and boundary bound states J. Phys. A: Math. Gen. 33 7661
95. White R, Affleck I and Scalapino J 2002 Friedel oscillations and charge density waves in chains and ladders Phys. Rev. B 65 165122
96. Gaudin M 1971 Boundary energy of a Bose gas in one dimension Phys. Rev. A 4 386
97. Alcaraz F C, Barber M N, Batchelor M T, Baxter R J and Quispel G R W 1987 Surface exponents of the quantum XXZ, Ashkin-Teller and Potts models J. Phys. A: Math. Gen. 20 6397
98. Sklyanin E K 1988 Boundary conditions for integrable quantum systems J. Phys. A: Math. Gen. 21 2375
99. Cherednik I V 1984 Factorizing particles on a half-line and root systems Theor. Math. Phys. 61 977
100. Kulish P P and Sklyanin E K 1991 The general Uq(sl2) invariant XXZ integrable quantum spin chain J. Phys. A: Math. Gen. 24 L435
101. Mezincescu L and Nepomechie R 1991 Integrability of open spin chains with quantum algebra symmetry Int. J. Mod. Phys. A 6 5231
102. Kulish P P and Sklyanin E K 1992 Algebraic structures related to reflection equations J. Phys. A: Math. Gen. 25 5963
103. Ghoshal S and Zamolodchikov A 1994 Boundary S-matrix and boundary state in 2-dimensional integrable quantum field theory Int. J. Mod. Phys. A 9 3841
104. Ghoshal S and Zamolodchikov A 1994 Int. J. Mod. Phys. A 9 4353
105. Fendley P and Saleur H 1994 Deriving boundary S-matrices Nucl. Phys. B 428 681
106. Skorik S and Saleur H 1995 Boundary bound states and boundary bootstrap in the sine-Gordon model with Dirichlet boundary condition J. Phys. A: Math. Gen. 28 6605
107. Leclair A, Mussardo G, Saleur H and Skorik S 1995 Boundary energy and boundary states in integrable quantum field theories Nucl. Phys. B 453 581
108. Kapustin A and Skorik S 1996 Surface excitations and surface energy of the antiferromagnetic XXZ chain by the Bethe ansatz approach J. Phys. A: Math. Gen. 29 1629
109. Lesage F, Saleur H and Skorik S 1996 Form factors approach to current correlations in one-dimensional systems with impurities Nucl. Phys. B 474 602
110. Wang Y-S 2000 The reconstruction of local quantum operators for the boundary XXZ spin-1/2 Heisenberg chain J. Phys. A: Math. Gen. 33 4009
111. Wang Y-S 2002 The scalar products and the norm of Bethe eigenstates for the boundary XXX Heisenberg spin-1/2 finite chain Nucl. Phys. B 622 633
112. Wang Y-S 2003 Boundary spontaneous polarization in the six-vertex model with a reflecting boundary J. Phys. A: Math. Gen. 36 4007
113. Slavnov N A 1989 Calculation of scalar products of wavefunction and form factors in the framework of the algebraic Bethe ansatz Theor. Math. Phys. 79 502
114. Tsuchiya O 1998 Determinant formula for the six-vertex model with reflecting end J. Math. Phys. 39 5946
115. Drinfel'd V G 1987 Quantum groups Proc. Int. Congress of Math. (Berkeley, USA, 1986) (Washington, DC: AMS) pp798-820