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Volumn 62, Issue 4, 2007, Pages 727-766

The algebraic Bethe ansatz and quantum integrable systems

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EID: 38149032783     PISSN: 00360279     EISSN: 14684829     Source Type: Journal    
DOI: 10.1070/RM2007v062n04ABEH004430     Document Type: Article
Times cited : (63)

References (51)
  • 1
    • 33846900525 scopus 로고
    • Zur Theorie der Metalle. I. Eigenwerte und Eigenfunktionen der linearen Atomkette
    • H. Bethe, "Zur Theorie der Metalle. I. Eigenwerte und Eigenfunktionen der linearen Atomkette", Z. Phys. 71:3-4 (1931), 205-226.
    • (1931) Z. Phys , vol.71 , Issue.3-4 , pp. 205-226
    • Bethe, H.1
  • 2
    • 0002076731 scopus 로고
    • Über das Austauschproblem eines Kristalls
    • L. Hulthén, "Über das Austauschproblem eines Kristalls", Ark. Mat. Astron. Fysik, vol. 26, 1938, pp. 1-106.
    • (1938) Ark. Mat. Astron. Fysik , vol.26 , pp. 1-106
    • Hulthén, L.1
  • 3
    • 36149006652 scopus 로고
    • Linear antiferromagnetic chain with anisotropic coupling
    • R. Orbach, "Linear antiferromagnetic chain with anisotropic coupling", Phys. Rev. 112:2 (1958), 309-316.
    • (1958) Phys. Rev , vol.112 , Issue.2 , pp. 309-316
    • Orbach, R.1
  • 4
    • 36149004524 scopus 로고
    • Antiferromagnetic linear chain
    • L. R. Walker, "Antiferromagnetic linear chain", Phys. Rev. 116:5 (1959), 1089 1090.
    • (1959) Phys. Rev , vol.116 , Issue.5 , pp. 1089-1090
    • Walker, L.R.1
  • 5
    • 85164636419 scopus 로고    scopus 로고
    • E. H. Lieb and W. Liniger, Exact analysis of an interacting Bose gas. I. The general solution and the ground state, Phys. Rev. 130:4 (1963), 1605-1616; E.H. Lieb, Exact analysis of an interacting Bose gas. II. The excitation spectrum, Phys. Rev. 130:4 (1963), 1616-1624.
    • E. H. Lieb and W. Liniger, "Exact analysis of an interacting Bose gas. I. The general solution and the ground state", Phys. Rev. 130:4 (1963), 1605-1616; E.H. Lieb, "Exact analysis of an interacting Bose gas. II. The excitation spectrum", Phys. Rev. 130:4 (1963), 1616-1624.
  • 7
    • 85164648561 scopus 로고    scopus 로고
    • C. N. Yang and C. P. Yang, One-dimensional chain of anisotropic spin-spin interactions. I. Proof of Bethe's hypothesis for ground state in a finite system, Phys. Rev. 150:1 (1966), 321-327; II. Properties of the ground state energy per lattice site in a finite system, 327-339.
    • C. N. Yang and C. P. Yang, "One-dimensional chain of anisotropic spin-spin interactions. I. Proof of Bethe's hypothesis for ground state in a finite system", Phys. Rev. 150:1 (1966), 321-327; "II. Properties of the ground state energy per lattice site in a finite system", 327-339.
  • 8
    • 2842602778 scopus 로고
    • Some exact results for the many-body problem in one dimension with repulsive delta-function interaction
    • C. N. Yang, "Some exact results for the many-body problem in one dimension with repulsive delta-function interaction", Phys. Rev. Lett. 19:23 (1967), 1312-1315.
    • (1967) Phys. Rev. Lett , vol.19 , Issue.23 , pp. 1312-1315
    • Yang, C.N.1
  • 9
    • 6144282458 scopus 로고
    • Anisotropic linear magnetic chain
    • J. des Cloizeaux and M. Gaudin, "Anisotropic linear magnetic chain", J. Math. Phys. 7:8 (1966), 1384-1400.
    • (1966) J. Math. Phys , vol.7 , Issue.8 , pp. 1384-1400
    • des Cloizeaux, J.1    Gaudin, M.2
  • 10
    • 0003965731 scopus 로고
    • La fonction d'onde, de Bethe
    • Collect. Commissariat Energ. Atom, Masson, Paris, French
    • M. Gaudin, La fonction d'onde, de Bethe, Collect. Commissariat Energ. Atom. Ser. Sci., Masson, Paris 1983. (French)
    • (1983) Ser. Sci
    • Gaudin, M.1
  • 11
    • 33747176055 scopus 로고
    • Relativistic two-dimensional model of a self-interacting fermion field with non-vanishing rest mass
    • F. A. Berezin and V. N. Sushko, "Relativistic two-dimensional model of a self-interacting fermion field with non-vanishing rest mass", Soviet Phys. JETP 21 (1965), 865.
    • (1965) Soviet Phys. JETP , vol.21 , pp. 865
    • Berezin, F.A.1    Sushko, V.N.2
  • 12
    • 0043141369 scopus 로고
    • Absence of Mott transition in an exact solution of the short range one band model in one dimension
    • E. H. Lieb and F. Y. Wu, "Absence of Mott transition in an exact solution of the short range one band model in one dimension", Phys. Rev. Lett. 20:25 (1968), 1445-1448.
    • (1968) Phys. Rev. Lett , vol.20 , Issue.25 , pp. 1445-1448
    • Lieb, E.H.1    Wu, F.Y.2
  • 13
    • 36149012281 scopus 로고
    • Crystal statistics. I. A two-dimensional model with an order-disorder transition
    • L. Onsager, "Crystal statistics. I. A two-dimensional model with an order-disorder transition", Phys. Rev. 65:3-4 (1944), 117-149.
    • (1944) Phys. Rev , vol.65 , Issue.3-4 , pp. 117-149
    • Onsager, L.1
  • 14
    • 0000715867 scopus 로고
    • Spin-spin correlation functions for the two-dimensional Ising model: Exact theory in the scaling region
    • T. T. Wu, B. M. McCoy, C. A. Tracy, and E. Barouch, "Spin-spin correlation functions for the two-dimensional Ising model: exact theory in the scaling region", Phys. Rev. B 13:1 (1976), 316-374.
    • (1976) Phys. Rev. B , vol.13 , Issue.1 , pp. 316-374
    • Wu, T.T.1    McCoy, B.M.2    Tracy, C.A.3    Barouch, E.4
  • 15
    • 20544432359 scopus 로고
    • Two-dimensional Ising model as an exactly solvable relativistic quantum field theory: Explicit formulas for n-point functions
    • B. M. McCoy, C. A. Tracy, and T. T. Wu, "Two-dimensional Ising model as an exactly solvable relativistic quantum field theory: explicit formulas for n-point functions", Phys. Rev. Lett. 38:15 (1977), 793-796.
    • (1977) Phys. Rev. Lett , vol.38 , Issue.15 , pp. 793-796
    • McCoy, B.M.1    Tracy, C.A.2    Wu, T.T.3
  • 16
    • 0008417829 scopus 로고
    • Two soluble models of an antiferromagnetic chain
    • E. Lieb, T. Shultz, and D. Mattis, "Two soluble models of an antiferromagnetic chain", Ann. Physics 16:3 (1961), 407-466.
    • (1961) Ann. Physics , vol.16 , Issue.3 , pp. 407-466
    • Lieb, E.1    Shultz, T.2    Mattis, D.3
  • 17
    • 23844537538 scopus 로고
    • Spin correlation functions of the X-Y model
    • B. M. McCoy, "Spin correlation functions of the X-Y model", Phys. Rev. 173:2 (1968), 531-541.
    • (1968) Phys. Rev , vol.173 , Issue.2 , pp. 531-541
    • McCoy, B.M.1
  • 18
    • 0142053350 scopus 로고
    • Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons
    • A. Lenard, "Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons", J. Math. Phys. 5:7 (1964), 930-943.
    • (1964) J. Math. Phys , vol.5 , Issue.7 , pp. 930-943
    • Lenard, A.1
  • 19
    • 0000799156 scopus 로고
    • One-dimensional impenetrable bosons in thermal equilibrium
    • A. Lenard, "One-dimensional impenetrable bosons in thermal equilibrium", J. Math. Phys. 7:7 (1966), 1268-1272.
    • (1966) J. Math. Phys , vol.7 , Issue.7 , pp. 1268-1272
    • Lenard, A.1
  • 20
    • 0002558504 scopus 로고
    • One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature
    • H. G. Vaidya and C. A. Tracy, "One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature", Phys. Rev. Lett. 42:1 (1979), 3-6.
    • (1979) Phys. Rev. Lett , vol.42 , Issue.1 , pp. 3-6
    • Vaidya, H.G.1    Tracy, C.A.2
  • 21
    • 34247358987 scopus 로고
    • Temperature correlation functions in the X X 0 Heisenberg chain. I
    • F. Colomo, A. G. Izergin, V. E. Korepin, and V. Tognetti, "Temperature correlation functions in the X X 0 Heisenberg chain. I", Theoret. and Math. Phys. 94:1 (1993), 11-38.
    • (1993) Theoret. and Math. Phys , vol.94 , Issue.1 , pp. 11-38
    • Colomo, F.1    Izergin, A.G.2    Korepin, V.E.3    Tognetti, V.4
  • 22
    • 85164648258 scopus 로고    scopus 로고
    • L. A. Takhtadzhan [Takhtajan] and L. D. Faddeev, The quantum method of the inverse problem and the Heisenberg X Y Z model, Russian Math. Surveys 34:5 (1979), 11-68.
    • L. A. Takhtadzhan [Takhtajan] and L. D. Faddeev, "The quantum method of the inverse problem and the Heisenberg X Y Z model", Russian Math. Surveys 34:5 (1979), 11-68.
  • 23
    • 85164642943 scopus 로고    scopus 로고
    • E. K. Sklyanin, L. A. Takhtadzhyan [Takhtajan], and L. D. Faddeev, Quantum inverse problem method. I, Theoret, and Math. Phys. 40:2 (1979), 688-706.
    • E. K. Sklyanin, L. A. Takhtadzhyan [Takhtajan], and L. D. Faddeev, "Quantum inverse problem method. I", Theoret, and Math. Phys. 40:2 (1979), 688-706.
  • 24
    • 0004335162 scopus 로고
    • How algebraic Bethe ansatz works for integrable models
    • Les Houches, France, eds, North-Holland, Amsterdam
    • L. D. Faddeev, "How algebraic Bethe ansatz works for integrable models", Symétries quantiques (Les Houches, France, 1995) (A. Connes et al., eds.), North-Holland, Amsterdam 1998, pp. 149-219.
    • (1995) Symétries quantiques , pp. 149-219
    • Faddeev, L.D.1
  • 25
    • 0033575637 scopus 로고    scopus 로고
    • Form factors of the X X Z Heisenberg spin-1/2 finite chain
    • 3 1999, arXiv: math-ph/9807020
    • N. Kitanine, J. M. Maillet, and V. Terras, "Form factors of the X X Z Heisenberg spin-1/2 finite chain", Nuclear Phys. B 554:3 (1999), 647-678; arXiv: math-ph/9807020, 1998.
    • (1998) Nuclear Phys. B , vol.554 , pp. 647-678
    • Kitanine, N.1    Maillet, J.M.2    Terras, V.3
  • 26
    • 85164649328 scopus 로고    scopus 로고
    • P. P. Kulish and E. K. Sklyanin, Quantum spectral transform method. Recent developments, Integrable quantum field theories (Tvärminne, Finland, 1981) (J. Heitarinta and C. Montonen, eds.), Lecture Notes in Phys., 151, Springer, Berlin-New York 1982, pp. 61-119.
    • P. P. Kulish and E. K. Sklyanin, "Quantum spectral transform method. Recent developments", Integrable quantum field theories (Tvärminne, Finland, 1981) (J. Heitarinta and C. Montonen, eds.), Lecture Notes in Phys., vol. 151, Springer, Berlin-New York 1982, pp. 61-119.
  • 27
    • 0002779065 scopus 로고
    • The quantum inverse scattering method approach to correlation functions
    • A. G. Izergin and V. E. Korepin, "The quantum inverse scattering method approach to correlation functions", Comm. Math. Phys. 94:1 (1984), 67-92.
    • (1984) Comm. Math. Phys , vol.94 , Issue.1 , pp. 67-92
    • Izergin, A.G.1    Korepin, V.E.2
  • 28
    • 33846349357 scopus 로고
    • Calculation of norms of Bethe wave functions
    • V. E. Korepin, "Calculation of norms of Bethe wave functions", Comm. Math. Phys. 86:3 (1982), 391-418.
    • (1982) Comm. Math. Phys , vol.86 , Issue.3 , pp. 391-418
    • Korepin, V.E.1
  • 29
    • 0039122423 scopus 로고
    • Analysis of the bilinear relation of a six-vertex model
    • V.E. Korepin, "Analysis of the bilinear relation of a six-vertex model", Soviet Phys. Dokl. 27:12 (1982), 1050-1051.
    • (1982) Soviet Phys. Dokl , vol.27 , Issue.12 , pp. 1050-1051
    • Korepin, V.E.1
  • 30
    • 0000152133 scopus 로고
    • Partition function of a six-vertex model in a finite volume
    • A. G. Izergin, "Partition function of a six-vertex model in a finite volume", Soviet Phys. Dokl. 32:11 (1987), 878-879.
    • (1987) Soviet Phys. Dokl , vol.32 , Issue.11 , pp. 878-879
    • Izergin, A.G.1
  • 31
    • 33751547286 scopus 로고    scopus 로고
    • History and perspectives of quantum groups
    • L. D. Faddeev, "History and perspectives of quantum groups", Milan J. Math. 74:1 (2006), 279-294.
    • (2006) Milan J. Math , vol.74 , Issue.1 , pp. 279-294
    • Faddeev, L.D.1
  • 33
    • 0000909580 scopus 로고
    • Method of the inverse scattering problem and the nonlinear quantum Schrödinger equation
    • E. K. Sklyanin, "Method of the inverse scattering problem and the nonlinear quantum Schrödinger equation", Soviet Phys. Dokl. 24 (1979), 107-109.
    • (1979) Soviet Phys. Dokl , vol.24 , pp. 107-109
    • Sklyanin, E.K.1
  • 34
    • 0001707729 scopus 로고
    • Quantum mechanical approach to completely integrable field theory models
    • E. K. Sklyanin and L. D. Faddeev, "Quantum mechanical approach to completely integrable field theory models", Soviet Phys. Dokl. 23 (1978), 902-904.
    • (1978) Soviet Phys. Dokl , vol.23 , pp. 902-904
    • Sklyanin, E.K.1    Faddeev, L.D.2
  • 35
    • 0001365048 scopus 로고
    • Pauli principal for one-dimensional bosons and the algebraic Bethe ansatz
    • A. G. Izergin and V. E. Korepin, "Pauli principal for one-dimensional bosons and the algebraic Bethe ansatz", Lett. Math. Phys. 6:4 (1982), 283-288.
    • (1982) Lett. Math. Phys , vol.6 , Issue.4 , pp. 283-288
    • Izergin, A.G.1    Korepin, V.E.2
  • 36
    • 84960593417 scopus 로고
    • Bases of Bethe vectors and difference equations with regular singular points
    • V. Tarasov and A. Varchenko, "Bases of Bethe vectors and difference equations with regular singular points", Internat. Math. Res. Notices 1995:13 (1995), 637-669.
    • (1995) Internat. Math. Res. Notices , vol.1995 , Issue.13 , pp. 637-669
    • Tarasov, V.1    Varchenko, A.2
  • 37
    • 15444377255 scopus 로고    scopus 로고
    • Master equation for spin-spin correlation functions of the X X Z chain
    • 3 2005, arXiv: hep-th/0406190
    • N. Kitanine, J. M. Maillet, N. A. Slavnov, and V. Terras, "Master equation for spin-spin correlation functions of the X X Z chain", Nucl. Phys. B 712:3 (2005), 600-622; arXiv: hep-th/0406190, 2004.
    • (2004) Nucl. Phys. B , vol.712 , pp. 600-622
    • Kitanine, N.1    Maillet, J.M.2    Slavnov, N.A.3    Terras, V.4
  • 38
    • 27544500636 scopus 로고
    • Calculation of scalar products of wave functions and form factors in the framework of the algebraic Bethe ansatz
    • N. A. Slavnov, "Calculation of scalar products of wave functions and form factors in the framework of the algebraic Bethe ansatz", Theoret, and Math. Phys. 79:2 (1989), 502-508.
    • (1989) Theoret, and Math. Phys , vol.79 , Issue.2 , pp. 502-508
    • Slavnov, N.A.1
  • 39
    • 0010693297 scopus 로고    scopus 로고
    • On an identity for dual fields
    • N. A. Slavnov, "On an identity for dual fields", J. Math. Sci. (New York) 100:2 (2000), 2181-2188.
    • (2000) J. Math. Sci. (New York) , vol.100 , Issue.2 , pp. 2181-2188
    • Slavnov, N.A.1
  • 40
    • 42749109039 scopus 로고    scopus 로고
    • On correlation functions of integrable models associated with the six-vertex R-matrix
    • arXiv: hep-th/0611142
    • N. Kitanine, K. Kozlowski, J. M. Maillet, N. A. Slavnov, and V. Terras, "On correlation functions of integrable models associated with the six-vertex R-matrix", J. Stat. Mech., 2007, no. 1, P01022; arXiv: hep-th/0611142, 2006.
    • (2006) J. Stat. Mech., 2007 , Issue.1
    • Kitanine, N.1    Kozlowski, K.2    Maillet, J.M.3    Slavnov, N.A.4    Terras, V.5
  • 41
    • 0347462915 scopus 로고
    • Zur Theorie des Ferromagnetismus
    • W. Heisenberg, "Zur Theorie des Ferromagnetismus", Z. Phys. 49:9-10 (1928), 619-636.
    • (1928) Z. Phys , vol.49 , Issue.9-10 , pp. 619-636
    • Heisenberg, W.1
  • 42
    • 0000689685 scopus 로고
    • Quantum inverse scattering method and the Heisenberg ferromagnet
    • P.P. Kulish and E. K. Sklyanin, "Quantum inverse scattering method and the Heisenberg ferromagnet", Phys. Lett. 70:5-6 (1979), 461-463.
    • (1979) Phys. Lett , vol.70 , Issue.5-6 , pp. 461-463
    • Kulish, P.P.1    Sklyanin, E.K.2
  • 43
    • 85164655369 scopus 로고    scopus 로고
    • [P.P. Kulish, The quantum inverse problem method and exactly solvable models of statistical physics, Proceedings of the 2nd International Symposium on selected problems of statistical physics, Dubna 1981, pp. 147-157.]
    • [P.P. Kulish, "The quantum inverse problem method and exactly solvable models of statistical physics", Proceedings of the 2nd International Symposium on selected problems of statistical physics, Dubna 1981, pp. 147-157.]
  • 44
    • 0001377186 scopus 로고
    • Correlation functions for the Heisenberg X X Z-antiferromagnet
    • A. G. Izergin and V. E. Korepin, "Correlation functions for the Heisenberg X X Z-antiferromagnet", Comm. Math. Phys. 99:2 (1985), 271-302.
    • (1985) Comm. Math. Phys , vol.99 , Issue.2 , pp. 271-302
    • Izergin, A.G.1    Korepin, V.E.2
  • 45
    • 0037078257 scopus 로고    scopus 로고
    • Spin-spin correlation functions of the X X Z-1/2 Heisenberg chain in a magnetic field
    • 3 2002, arXiv: hep-th/0201045
    • N. Kitanine, J. M. Maillet, N. A. Slavnov, and V. Terras, "Spin-spin correlation functions of the X X Z-1/2 Heisenberg chain in a magnetic field", Nucl. Phys. B 641:3 (2002), 487-518; arXiv: hep-th/0201045, 2002.
    • (2002) Nucl. Phys. B , vol.641 , pp. 487-518
    • Kitanine, N.1    Maillet, J.M.2    Slavnov, N.A.3    Terras, V.4
  • 46
    • 0034695772 scopus 로고    scopus 로고
    • Correlation functions of the X X Z Heisenberg spin-1/2 chain in a magnetic field
    • 3 2000, arXiv: math-ph/9907019
    • N. Kitanine, J. M. Maillet, and V. Terras, "Correlation functions of the X X Z Heisenberg spin-1/2 chain in a magnetic field", Nucl. Phys. B 567:3 (2000), 554-582; arXiv: math-ph/9907019, 1999.
    • (1999) Nucl. Phys. B , vol.567 , pp. 554-582
    • Kitanine, N.1    Maillet, J.M.2    Terras, V.3
  • 47
    • 0038467297 scopus 로고    scopus 로고
    • Emptiness formation probability of the X X Z spin-1/2 Heisenberg chain at δ = 1/2
    • 27 2002, arXiv: hep-th/0201134
    • N. Kitanine, J. M. Maillet, N. A. Slavnov, and V. Terras, "Emptiness formation probability of the X X Z spin-1/2 Heisenberg chain at δ = 1/2", J. Phys. A Math. Gen. 35:27 (2002), L385-L388; arXiv: hep-th/0201134, 2002.
    • (2002) J. Phys. A Math. Gen , vol.35
    • Kitanine, N.1    Maillet, J.M.2    Slavnov, N.A.3    Terras, V.4
  • 48
    • 1842529920 scopus 로고    scopus 로고
    • Another proof of the alternating sign matrix conjecture
    • 3 1996, arXiv: math.CO/9712207
    • G. Kuperberg, "Another proof of the alternating sign matrix conjecture", Internat. Math. Res. Notices 1996:3 (1996), 139-150; arXiv: math.CO/9712207, 1997.
    • (1996) Internat. Math. Res. Notices , pp. 139-150
    • Kuperberg, G.1
  • 49
    • 0035853651 scopus 로고    scopus 로고
    • Spin chains and combinatorics
    • 14 2001, arXiv: cond-mat/0012141
    • A. Razumov and Yu. Stroganov, "Spin chains and combinatorics", J. Phys. A Math. Gen. 34:14 (2001), 3185-3190; arXiv: cond-mat/0012141, 2000.
    • (2000) J. Phys. A Math. Gen , vol.34 , pp. 3185-3190
    • Razumov, A.1    Stroganov, Y.2
  • 50
    • 0011630061 scopus 로고
    • Partition function of the eight-vertex lattice model
    • R. J. Baxter, "Partition function of the eight-vertex lattice model", Ann. Physics 70:1 (1972), 193-228.
    • (1972) Ann. Physics , vol.70 , Issue.1 , pp. 193-228
    • Baxter, R.J.1
  • 51
    • 0002152395 scopus 로고    scopus 로고
    • R. J. Baxter, Eight-vertex model in lattice statistics and one-dimensional anisotropic Heisenberg chain. I. Some fundamental eigenvectors, Ann. Physics 76:1 (1973), 1-24; II. Equivalence to a generalized ice-type lattice model, 25-47; III. Eigenvectors of the transfer matrix and hamiltonian, 48-71.
    • R. J. Baxter, "Eight-vertex model in lattice statistics and one-dimensional anisotropic Heisenberg chain. I. Some fundamental eigenvectors", Ann. Physics 76:1 (1973), 1-24; "II. Equivalence to a generalized ice-type lattice model", 25-47; "III. Eigenvectors of the transfer matrix and hamiltonian", 48-71.


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