Exact solution of the Izergin-Korepin model with general non-diagonal boundary terms
详细信息 查看全文
- 作者：Kun Hao (1)
Junpeng Cao (2) (3)
Guang-Liang Li (4)
Wen-Li Yang (1) (5)
Kangjie Shi (1)
Yupeng Wang (2) (3)
1. Institute of Modern Physics ; Northwest University ; Xian ; 710069 ; China
2. Beijing National Laboratory for Condensed Matter Physics ; Institute of Physics ; Chinese Academy of Sciences ; Beijing ; 100190 ; China
3. Collaborative Innovation Center of Quantum Matter ; Beijing ; China
4. Department of Applied Physics ; Xian Jiaotong University ; Xian ; 710049 ; China
5. Beijing Center for Mathematics and Information Interdisciplinary Sciences ; Beijing ; 100048 ; China - 关键词：Bethe Ansatz ; Lattice Integrable Models
- 刊名：Journal of High Energy Physics
- 出版年：2014
- 出版时间：June 2014
- 年：2014
- 卷：2014
- 期：6
- 全文大小：562 KB
- 参考文献：1. R.J. Baxter, / Exactly Solved Models in Statistical Mechanics, Academic Press, (1982).
2. Dolan, L, Nappi, CR, Witten, E (2003) A Relation between approaches to integrability in superconformal Yang-Mills theory. JHEP 10: pp. 017 CrossRef
3. Beisert, N (2012) Review of AdS/CFT integrability: an overview. Lett. Math. Phys. 99: pp. 3 CrossRef
4. Zvyagin, AA (2005) Finite Size Effects in Correlated Electron Models: Exact Results. Imperial College Press, London, U.K CrossRef
5. Guan, X-W, Batchelor, MT, Lee, C (2013) Fermi gases in one dimension: From Bethe ansatz to experiments. Rev. Mod. Phys. 85: pp. 1633 CrossRef
6. Gier, J, Essler, FHL (2005) Bethe Ansatz Solution of the Asymmetric Exclusion Process with Open Boundaries. Phys. Rev. Lett. 95: pp. 240601 CrossRef
7. J. de Gier and F.H.L. Essler, / Exact spectral gaps of the asymmetric exclusion process with open boundaries, / J. Stat. Mech. (2006) P12011 [cond-mat/0609645].
8. Sirker, J, Pereira, RG, Affleck, I (2009) Diffusion and ballistic transport in one-dimensional quantum systems. Phys. Rev. Lett. 103: pp. 216602 CrossRef
9. Takhtadzhan, LA, Faddeev, LD (1979) The quantum method of the inverse problem and the Heisenberg XYZ model. Russ. Math. Sur. 34: pp. 11 CrossRef
10. Yung, CM, Batchelor, MT (1995) Exact solution for the spin s XXZ quantum chain with nondiagonal twists. Nucl. Phys. B 446: pp. 461 CrossRef
11. Nepomechie, RI (2001) Bethe Ansatz solution of the open XX spin chain with nondiagonal boundary terms. J. Phys. A 34: pp. 9993
12. Nepomechie, RI (2002) Solving the open XXZ spin chain with nondiagonal boundary terms at roots of unity. Nucl. Phys. B 622: pp. 615 CrossRef
13. Nepomechie, RI (2003) Functional relations and Bethe Ansatz for the XXZ chain. J. Statist. Phys. 111: pp. 1363 CrossRef
14. Nepomechie, RI (2004) Bethe ansatz solution of the open XXZ chain with nondiagonal boundary terms. J. Phys. A 37: pp. 433
15. Cao, J, Lin, H-Q, Shi, K-J, Wang, Y (2003) Exact solution of XXZ spin chain with unparallel boundary fields. Nucl. Phys. B 663: pp. 487 CrossRef
16. Yang, WL, Sasaki, R (2004) Solution of the dual reflection equation for A n 鈭1 1 $$ {A}_{n-1}^{(1)} $$ SOS model. J. Math. Phys. 45: pp. 4301 CrossRef
17. Yang, WL, Sasaki, R (2004) Exact solution of Z(n) Belavin model with open boundary condition. Nucl. Phys. B 679: pp. 495 CrossRef
18. Galleas, W, Martins, MJ (2005) Solution of the SU(N) vertex model with non-diagonal open boundaries. Phys. Lett. A 335: pp. 167 CrossRef
19. Yang, W-L, Zhang, Y-Z (2004) Non-diagonal solutions of the reflection equation for the trigonometric A n 鈭1 1 $$ {A}_{n-1}^{(1)} $$ vertex model. JHEP 12: pp. 019 CrossRef
20. Yang, W-L, Zhang, Y-Z (2005) Exact solution of the A n 鈭1 1 $$ {A}_{n-1}^{(1)} $$ trigonometric vertex model with non-diagonal open boundaries. JHEP 01: pp. 021 CrossRef
21. Cao, J, Yang, W-L, Shi, K, Wang, Y (2014) Nested off-diagonal Bethe ansatz and exact solutions of the SU(N ) spin chain with generic integrable boundaries. JHEP 04: pp. 143 CrossRef
22. Bethe, H (1931) On the theory of metals. 1. Eigenvalues and eigenfunctions for the linear atomic chain. Z. Phys. 71: pp. 205 CrossRef
23. Alcaraz, FC, Barber, MN, Batchelor, MT, Baxter, RJ, Quispel, GRW (1987) Surface Exponents of the Quantum XXZ, Ashkin-Teller and Potts Models. J. Phys. A 20: pp. 6397
24. Baxter, RJ (1971) Eight-Vertex Model in Lattice Statistics. Phys. Rev. Lett. 26: pp. 832 CrossRef
25. Baxter, RJ (1971) One-Dimensional Anisotropic Heisenberg Chain. Phys. Rev. Lett. 26: pp. 834 CrossRef
26. Baxter, RJ (1972) One-dimensional anisotropic Heisenberg chain. Annals Phys. 70: pp. 323 CrossRef
27. Sklyanin, EK, Faddeev, LD (1978) Quantum Mechanical Approach to Completely Integrable Field Theory Models. Sov. Phys. Dokl. 23: pp. 902
28. Sklyanin, EK (1988) Boundary Conditions for Integrable Quantum Systems. J. Phys. A 21: pp. 2375
29. J. de Gier and P. Pyatov, / Bethe ansatz for the Temperley-Lieb loop model with open boundaries, / J. Stat. Mech. (2004) P03002 [hep-th/0312235] [INSPIRE].
30. A. Nichols, V. Rittenberg and J. de Gier, / One-boundary Temperley-Lieb algebras in the XXZ and loop models, / J. Stat. Mech. (2005) P03003 [cond-mat/0411512] [INSPIRE].
31. Gier, J, Nichols, A, Pyatov, P, Rittenberg, V (2005) Magic in the spectra of the XXZ quantum chain with boundaries at 螖 = 0 and 螖 = 鈭?/2. Nucl. Phys. B 729: pp. 387 CrossRef
32. Yang, W-L, Zhang, Y-Z, Gould, MD (2004) Exact solution of the XXZ Gaudin model with generic open boundaries. Nucl. Phys. B 698: pp. 503 CrossRef
33. A. Doikou and P.P. Martin, / On quantum group symmetry and Bethe ansatz for the asymmetric twin spin chain with integrable boundary, / J. Stat. Mech. (2006) P06004 [hep-th/0503019] [INSPIRE].
34. A. Doikou, / The Open XXZ and associated models at q root of unity, / J. Stat. Mech. (2006) P09010 [hep-th/0603112] [INSPIRE].
35. Z. Bajnok, / Equivalences between spin models induced by defects, / J. Stat. Mech. (2006) P06010 [hep-th/0601107] [INSPIRE].
36. P. Baseilhac and K. Koizumi, / Exact spectrum of the XXZ open spin chain from the q-Onsager algebra representation theory, / J. Stat. Mech. (2007) P09006 [hep-th/0703106] [INSPIRE].
37. Yang, W-L, Nepomechie, RI, Zhang, Y-Z (2006) Q-operator and T-Q relation from the fusion hierarchy. Phys. Lett. B 633: pp. 664 CrossRef
38. Galleas, W (2008) Functional relations from the Yang-Baxter algebra: Eigenvalues of the XXZ model with non-diagonal twisted and open boundary conditions. Nucl. Phys. B 790: pp. 524 CrossRef
39. Frahm, H, Seel, A, Wirth, T (2008) Separation of Variables in the open XXX chain. Nucl. Phys. B 802: pp. 351 CrossRef
40. G. Niccoli, / Non-diagonal open spin-1/2 XXZ quantum chains by separation of variables: Complete spectrum and matrix elements of some quasi-local operators, / J. Stat. Mech. (2012) P10025 [arXiv:1206.0646] [INSPIRE].
41. Niccoli, G (2013) Antiperiodic spin-1/2 XXZ quantum chains by separation of variables: Complete spectrum and form factors. Nucl. Phys. B 870: pp. 397 CrossRef
42. Niccoli, G (2013) Antiperiodic dynamical 6-vertex and periodic 8-vertex models I: Complete spectrum by SOV and matrix elements of the identity on separate states. J. Phys. A 46: pp. 075003
43. Cao, J, Yang, W, Shi, K, Wang, Y (2013) Off-diagonal Bethe ansatz and exact solution of a topological spin ring. Phys. Rev. Lett. 111: pp. 137201 CrossRef
44. Cao, J, Yang, W-L, Shi, K, Wang, Y (2013) Off-diagonal Bethe ansatz solution of the XXX spin-chain with arbitrary boundary conditions. Nucl. Phys. B 875: pp. 152
45. J. Cao, W.-L. Yang, K.-J. Shi and u. Wang, / Spin-1/2 XYZ model revisit: general solutions via off-diagonal Bethe ansatz, arXiv:1307.0280 [INSPIRE].
46. Cao, J, Yang, W-L, Shi, K, Wang, Y (2013) Off-diagonal Bethe ansatz solutions of the anisotropic spin- 1 2 $$ \frac{1}{2} $$ chains with arbitrary boundary fields. Nucl. Phys. B 877: pp. 152
47. Baseilhac, P (2006) The q-deformed analogue of the Onsager algebra: Beyond the Bethe ansatz approach. Nucl. Phys. B 754: pp. 309 CrossRef
48. Baseilhac, P, Belliard, S (2013) The half-infinite XXZ chain in Onsager鈥檚 approach. Nucl. Phys. B 873: pp. 550 CrossRef
49. P. Baseilhac and T. Kojima, / Form factors of the half-infinite XXZ spin chain with a triangular boundary, arXiv:1404.0491 [INSPIRE].
50. Li, Y-Y, Cao, J, Yang, W-L, Shi, K, Wang, Y (2014) Exact solution of the one-dimensional Hubbard model with arbitrary boundary magnetic fields. Nucl. Phys. B 879: pp. 98 CrossRef
51. X. Zhang, J. Cao, W.-L. Yang, K. Shi and Y. Wang, / Exact solution of the one-dimensional super-symmetric t-J model with unparallel boundary fields, / J. Stat. Mech. (2014) P04031 [arXiv:1312.0376] [INSPIRE].
52. Nepomechie, RI (2013) An inhomogeneous T-Q equation for the open XXX chain with general boundary terms: completeness and arbitrary spin. J. Phys. A 46: pp. 442002
53. Y. Jiang, S. Cui, J. Cao, W.-L. Yang and Y. Wang, / Completeness and Bethe root distribution of the spin-1/2 Heisenberg chain with arbitrary boundary fields, arXiv:1309.6456 [INSPIRE].
54. S. Faldella, N. Kitanine and G. Niccoli, / Complete spectrum and scalar products for the open spin-1/2 XXZ quantum chains with non-diagonal boundary terms, / J. Stat. Mech. (2014) P01011 [arXiv:1307.3960] [INSPIRE].
55. Kitanine, N, Maillet, J-M, Niccoli, G (2014) Open spin chains with generic integrable boundaries: Baxter equation and Bethe ansatz completeness from separation of variables. J. Stat. Mech. 1405: CrossRef
56. S. Belliard and N. Cramp茅, / Heisenberg XXX Model with General Boundaries: Eigenvectors from Algebraic Bethe Ansatz, / SIGMA (2013) 072.
57. Izergin, AG, Korepin, VE (1981) The inverse scattering method approach to the quantum Shabat-Mikhailov model. Commun. Math. Phys. 79: pp. 303 CrossRef
58. Dodd, RK, Bullough, RK (1977) Polynomial Conserved Densities for the sine-Gordon Equations. Proc. Roy. Soc. Lond. A 352: pp. 481 CrossRef
59. Zhiber, AV, Shabat, AB (1979) Klein-Gordon equations with a nontrivial group. Sov. Phys. Dokl. 24: pp. 607
60. Yung, CM, Batchelor, MT (1995) Integrable vertex and loop models on the square lattice with open boundaries via reflection matrices. Nucl. Phys. B 435: pp. 430 CrossRef
61. Batchelor, MT, Yung, CM (1995) Exact Results for the Adsorption of a Flexible Self-Avoiding Polymer Chain in Two Dimensions. Phys. Rev. Lett. 74: pp. 2026 CrossRef
62. Reshetikhin, NY (1983) The functional equation method in the theory of exactly soluble quantum systems. Sov. Phys. JETP 57: pp. 691
63. Tarasov, VA (1988) Algebraic Bethe ansatz for the Izergin-Korepin R-matrix. Theor. Math. Phys. 76: pp. 793 CrossRef
64. J.D. Kim, / Boundary K matrix for the quantum Mikhailov-Shabat model, hep-th/9412192 [INSPIRE].
65. Martins, MJ (1995) The Exact solution and the finite size behavior of the Osp(1/2) invariant spin chain. Nucl. Phys. B 450: pp. 768 CrossRef
66. Mezincescu, L, Nepomechie, RI (1992) Analytical Bethe Ansatz for quantum algebra invariant spin chains. Nucl. Phys. B 372: pp. 597 CrossRef
67. Fan, H (1997) Bethe ansatz for the Izergin-Korepin model. Nucl. Phys. B 488: pp. 409 CrossRef
68. Hou, B-Y, Yang, W-L, Zhang, Y-Z (1999) The twisted quantum affine algebra U q A 2 2 $$ {U}_q\left({A}_2^{(2)}\right) $$ and correlation functions of the Izergin-Korepin model. Nucl. Phys. B 556: pp. 485 CrossRef
69. Lima-Santos, A (1999) Reflection K-matrices for 19-vertex models. Nucl. Phys. B 558: pp. 637 CrossRef
70. Yang, W-L, Zhang, Y-Z (2001) Izergin-Korepin model with a boundary. Nucl. Phys. B 596: pp. 495 CrossRef
71. Nepomechie, RI (2002) Boundary quantum group generators of type A. Lett. Math. Phys. 62: pp. 83 CrossRef
72. Li, G-L, Shi, K-J, Yue, R-H (2003) The algebraic Bethe ansatz for the Izergin-Korepin model with open boundary conditions. Nucl. Phys. B 670: pp. 401 CrossRef
73. Mezincescu, L, Nepomechie, RI (1991) Integrability of open spin chains with quantum algebra symmetry. Int. J. Mod. Phys. A 6: pp. 5231 CrossRef
74. Karowski, M (1979) On the Bound State Problem in (1+1)-dimensional Field Theories. Nucl. Phys. B 153: pp. 244 CrossRef
75. Kulish, PP, Reshetikhin, NY, Sklyanin, EK (1981) Yang-Baxter Equation and Representation Theory. 1. Lett. Math. Phys. 5: pp. 393 CrossRef
76. Kulish, PP, Sklyanin, EK (1982) Quantum spectral transform method recent developments. Lect. Notes Phys. 151: pp. 61 CrossRef
77. Kirillov, AN, Reshetikhin, NY (1986) Exact solution of the Heisenberg XXZ model of spin s. J. Sov. Math. 35: pp. 2627 CrossRef
78. Kirillov, AN, Reshetikhin, NY (1987) Exact solution of the integrable XXZ Heisenberg model with arbitrary spin. I. The ground state and the excitation spectrum. J. Phys. A 20: pp. 1565
79. Zhou, Y-k (1996) Row transfer matrix functional relations for Baxter鈥檚 eight vertex and six vertex models with open boundaries via more general reflection matrices. Nucl. Phys. B 458: pp. 504 CrossRef
80. Kulish, PP, Sklyanin, EK (1979) Quantum inverse scattering method and the Heisenberg ferromagnet. Phys. Lett. A 70: pp. 461 CrossRef
81. Chari, V, Pressley, A (1994) A Guide to Quantum Groups. Cambridge University Press, Cambridge
82. Yang, W-L, Zhang, Y-Z (2006) T-Q relation and exact solution for the XYZ chain with general nondiagonal boundary terms. Nucl. Phys. B 744: pp. 312 CrossRef
83. Yang, W-L, Zhang, Y-Z (2007) On the second reference state and complete eigenstates of the open XXZ chain. JHEP 04: pp. 044 CrossRef
84. Nepomechie, RI, Ravanini, F (2003) Completeness of the Bethe ansatz solution of the open XXZ chain with nondiagonal boundary terms. J. Phys. A 36: pp. 11391
85. Nepomechie, RI, Ravanini, F (2004) Addendum to 鈥楥ompleteness of the Bethe Ansatz solution of the open XXZ chain with nondiagonal boundary terms鈥? J. Phys. A 37: pp. 1945
86. Korepin, VE, Boliubov, NM, Izergin, AG (1993) Quantum Inverse Scattering Method and Correlation Functions. Cambridge University Press, Cambridge CrossRef
87. Takahashi, M (1999) Thermodynamics of One-Dimensional Solvable Models. Cambridge University Press, Cambridge CrossRef
88. Li, Y-Y, Cao, J, Yang, W-L, Shi, K, Wang, Y (2014) Thermodynamic limit and surface energy of the XXZ spin chain with arbitrary boundary fields. Nucl. Phys. B 884: pp. 17 CrossRef - 刊物类别：Physics and Astronomy
- 刊物主题：Physics
Elementary Particles and Quantum Field Theory
Quantum Field Theories, String Theory - 出版者：Springer Berlin / Heidelberg
- ISSN：1029-8479
文摘