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The Nested Off-Diagonal Bethe Ansatz

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Off-Diagonal Bethe Ansatz for Exactly Solvable Models
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Abstract

In Chap. 2, we introduced how the nested algebraic Bethe Ansatz method was used in the exact solution of the periodic \(SU(n)\)-invariant spin chain. This method can also solve the open chain with diagonal boundaries [15].

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References

  1. A. Doikou, Fusion and analytical Bethe Ansatz for the \(A_{n-1}^{(1)}\) open spin chain. J. Phys. A 33, 4755 (2000)

    Article  ADS  MATH  MathSciNet  Google Scholar 

  2. A. Doikou, R.I. Nepomechie, Duality and quantum-algebra symmetry of the \(A_{N-1}^{(1)}\) open spin chain with diagonal boundary fields. Nucl. Phys. B 530, 641 (1998)

    Article  ADS  MATH  MathSciNet  Google Scholar 

  3. A. Doikou, R.I. Nepomechie, Bulk and boundary S matrices for the \(SU(N)\) chain. Nucl. Phys. B 521, 547 (1998)

    Article  ADS  MATH  MathSciNet  Google Scholar 

  4. H.J. de Vega, A. Gonz\(\acute{a}\)lez-Ruiz, Exact solution of the \(SU_q(n)\)-invariant quantum spin chains. Nucl. Phys. B 417, 553 (1994)

    Google Scholar 

  5. H.J. de Vega, A. Gonz\(\acute{a}\)lez-Ruiz, Exact Bethe Ansatz solution for \(A_{n-1}\) chains with non-\(SU_q(n)\) invariant open boundary conditions. Mod. Phys. Lett. A 09, 2207 (1994)

    Google Scholar 

  6. S. Belliard, N. Crampé, Heisenberg XXX model with general boundaries: eigenvectors from algebraic Bethe Ansatz. SIGMA 9, 072 (2013)

    Google Scholar 

  7. J. Cao, W.-L. Yang, K. Shi, Y. Wang, Nested off-diagonal Bethe Ansatz and exact solutions of the \(su(n)\) spin chain with generic integrable boundaries. J. High Energy Phys. 04, 143 (2014)

    Article  ADS  Google Scholar 

  8. M. Karowski, On the bound state problem in \(1+1\) dimensional field theories. Nucl. Phys. B 153, 244 (1979)

    Article  ADS  Google Scholar 

  9. P.P. Kulish, N.Y. Reshetikhin, E.K. Sklyanin, Yang-Baxter equation and representation theory: I. Lett. Math. Phys. 5, 393 (1981)

    Google Scholar 

  10. P.P. Kulish, E.K. Sklyanin, Quantum spectral transform method: recent developments. Lect. Notes Phys. 151, 61 (1982)

    Article  ADS  MathSciNet  Google Scholar 

  11. A.N. Kirillov, N.Y. Reshetikhin, Exact solution of the Heisenberg XXZ model of spin \(s\). J. Sov. Math. 35, 2627 (1986)

    Google Scholar 

  12. A.N. Kirillov, N.Y. Reshetikhin, Exact solution of the integrable XXZ Heisenberg model with arbitrary spin. I. The ground state and the excitation spectrum. J. Phys. A 20, 1565 (1987)

    Google Scholar 

  13. B. Sutherland, Model for a multicomponent quantum system. Phys. Rev. B 12, 3795 (1975)

    Article  ADS  Google Scholar 

  14. H.J. De Vega, E. Lopes, Exact solution of the Perk-Schultz model. Phys. Rev. Lett. 67, 489 (1991)

    Google Scholar 

  15. E. Lopes, Exact solution of the multi-component generalized six-vertex model. Nucl. Phys. B 370, 636 (1992)

    Article  ADS  MathSciNet  Google Scholar 

  16. I. Krichever, O. Lipan, P. Wiegmann, A. Zabrodin, Quantum integrable systems and elliptic solutions of classical discrete nonlinear equations. Commun. Math. Phys. 188, 267 (1997)

    Article  ADS  MATH  MathSciNet  Google Scholar 

  17. H. Frahm, N.A. Slavnov, New solutions to the reflection equation and the projecting method. J. Phys. A 32, 1547 (1999)

    Article  ADS  MATH  MathSciNet  Google Scholar 

  18. W. Galleas, M.J. Martins, Solution of the \(SU(N)\) vertex model with non-diagonal open boundaries. Phys. Lett. A 335, 167 (2005)

    Article  ADS  MATH  MathSciNet  Google Scholar 

  19. H.J. de Vega, A. González-Ruiz, Boundary K-matrices for the XYZ, XXZ and XXX spin chains. J. Phys. A 27, 6129 (1994)

    Google Scholar 

  20. P.P. Kulish, Yang-Baxter equation and reflection equations in integrable models, arXiv:hep-th/9507070

  21. L. Mezincescu, R.I. Nepomechie, Fusion procedure for open chains. J. Phys. A 25, 2533 (1992)

    Article  ADS  MathSciNet  Google Scholar 

  22. Y.-K. Zhou, Row transfer matrix functional relations for Baxter’s eight-vertex and six-vertex models with open boundaries via more general reflection matrices. Nucl. Phys. B 458, 504 (1996)

    Google Scholar 

  23. P.P. Kulish, E.K. Sklyanin, Quantum inverse scattering method and the Heisenberg ferromagnet. Phys. Lett. A 70, 461 (1979)

    Google Scholar 

  24. E.K. Sklyanin, Boundary conditions for integrable quantum systems. J. Phys. A 21, 2375 (1988)

    Article  ADS  MATH  MathSciNet  Google Scholar 

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Correspondence to Yupeng Wang .

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Wang, Y., Yang, WL., Cao, J., Shi, K. (2015). The Nested Off-Diagonal Bethe Ansatz. In: Off-Diagonal Bethe Ansatz for Exactly Solvable Models. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-46756-5_7

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  • DOI: https://doi.org/10.1007/978-3-662-46756-5_7

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