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TMF, 1989, Volume 79, Number 2, Pages 232–240 (Mi tmf4872)  

This article is cited in 51 scientific papers (total in 51 papers)

Calculation of scalar products of wave functions and form factors in the framework of the algebraic Bethe ansatz

N. A. Slavnov

Abstract: Explicit formulas are obtained for one particular case of the scalar products of wave functions and the formf actor of the particle number operator in the generalized two-dimensional model

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English version:
Theoretical and Mathematical Physics, 1989, 79:2, 502–508

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Received: 08.06.1988

Citation: N. A. Slavnov, “Calculation of scalar products of wave functions and form factors in the framework of the algebraic Bethe ansatz”, TMF, 79:2 (1989), 232–240; Theoret. and Math. Phys., 79:2 (1989), 502–508

Citation in format AMSBIB
\by N.~A.~Slavnov
\paper Calculation of~scalar products of~wave functions and form factors in~the framework of~the algebraic Bethe ansatz
\jour TMF
\yr 1989
\vol 79
\issue 2
\pages 232--240
\jour Theoret. and Math. Phys.
\yr 1989
\vol 79
\issue 2
\pages 502--508

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    This publication is cited in the following articles:
    1. N. A. Slavnov, “Nonequal-time current correlation function in a one-dimensional Bose gas”, Theoret. and Math. Phys., 82:3 (1990), 273–282  mathnet  crossref  mathscinet  isi
    2. N. A. Slavnov, “Cancellation of dual fields in free fermion models with trigonometric $R$-matrix”, Theoret. and Math. Phys., 108:2 (1996), 993–1002  mathnet  crossref  crossref  mathscinet  zmath  isi
    3. V. E. Korepin, N. A. Slavnov, “The Form Factors in a Finite Volume”, Proc. Steklov Inst. Math., 226 (1999), 72–85  mathnet  mathscinet  zmath
    4. N. A. Slavnov, “Integral Representations for Correlation Functions of the $XXZ$ Heisenberg Chain”, Theoret. and Math. Phys., 135:3 (2003), 828–835  mathnet  crossref  crossref  mathscinet  zmath  isi
    5. N. A. Slavnov, “On Scalar Products in the Algebraic Bethe Ansatz”, Proc. Steklov Inst. Math., 251 (2005), 246–253  mathnet  mathscinet  zmath
    6. P. P. Kulish, P. D. Ryasichenko, “Spin chain connected to the quantum superalgebra $\mathrm{sl}_q(1\mid 1)$”, J. Math. Sci. (N. Y.), 138:3 (2006), 5711–5721  mathnet  crossref  mathscinet  zmath
    7. N. A. Slavnov, “The algebraic Bethe ansatz and quantum integrable systems”, Russian Math. Surveys, 62:4 (2007), 727–766  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    8. Caux, JS, “One-particle dynamical correlations in the one-dimensional Bose gas”, Journal of Statistical Mechanics-Theory and Experiment, 2007, P01008  isi
    9. Samuel Belliard, Stanislav Pakuliak, Eric Ragoucy, “Universal Bethe Ansatz and Scalar Products of Bethe Vectors”, SIGMA, 6 (2010), 094, 22 pp.  mathnet  crossref  mathscinet
    10. Dunning C., Ibanez M., Links J., Sierra G., Zhao Sh.-Y., “Exact solution of the p plus ip pairing Hamiltonian and a hierarchy of integrable models”, J Stat Mech Theory Exp, 2010, P08025  isi
    11. Gritsev V., Rostunov T., Demler E., “Exact methods in the analysis of the non-equilibrium dynamics of integrable models: application to the study of correlation functions for non-equilibrium 1D Bose gas”, J Stat Mech Theory Exp, 2010, P05012  isi
    12. Tetsuo Deguchi, Jun Sato, “Quantum Group $U_q(sl(2))$ Symmetry and Explicit Evaluation of the One-Point Functions of the Integrable Spin-1 XXZ Chain”, SIGMA, 7 (2011), 056, 41 pp.  mathnet  crossref  mathscinet
    13. Kitanine N., Kozlowski K.K., Maillet J.M., Slavnov N.A., Terras V., “The thermodynamic limit of particle-hole form factors in the massless XXZ Heisenberg chain”, J Stat Mech Theory Exp, 2011, P05028  isi
    14. Kozlowski K.K., Terras V., “Long-time and large-distance asymptotic behavior of the current-current correlators in the non-linear Schrodinger model”, J Stat Mech Theory Exp, 2011, P09013  isi
    15. Gavrylenko P., Iorgov N., Lisovyy O., “Form factors of twist fields in the lattice Dirac theory”, J. Phys. A: Math. Theor., 45:2 (2012), 025402  crossref  isi
    16. Foda O. Wheeler M., “Partial Domain Wall Partition Functions”, J. High Energy Phys., 2012, no. 7, 186  crossref  isi
    17. Samuel Belliard, Stanislav Pakuliak, Eric Ragoucy, Nikita A. Slavnov, “Bethe Vectors of Quantum Integrable Models with $\mathrm{GL}(3)$ Trigonometric $R$-Matrix”, SIGMA, 9 (2013), 058, 23 pp.  mathnet  crossref  mathscinet
    18. Motegi K. Sakai K., “Vertex Models, Tasep and Grothendieck Polynomials”, J. Phys. A-Math. Theor., 46:35 (2013), 355201  crossref  isi
    19. Belliard S. Pakuliak S. Ragoucy E. Slavnov N.A., “Bethe Vectors of Gl(3)-Invariant Integrable Models”, J. Stat. Mech.-Theory Exp., 2013, P02020  crossref  isi
    20. S. Z. Pakulyak, E. Ragoucy, N. A. Slavnov, “Scalar products in models with a $GL(3)$ trigonometric $R$-matrix: Highest coefficient”, Theoret. and Math. Phys., 178:3 (2014), 314–335  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    21. S. Z. Pakulyak, E. Ragoucy, N. A. Slavnov, “Scalar products in models with the $GL(3)$ trigonometric $R$-matrix: General case”, Theoret. and Math. Phys., 180:1 (2014), 795–814  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib  elib
    22. S. Z. Pakulyak, E. Ragoucy, N. A. Slavnov, “Determinant representations for form factors in quantum integrable models with the $GL(3)$-invariant $R$-matrix”, Theoret. and Math. Phys., 181:3 (2014), 1566–1584  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib  elib
    23. Hagendorf Ch., “The Nineteen-Vertex Model and Alternating Sign Matrices”, J. Stat. Mech.-Theory Exp., 2015, P01017  crossref  isi
    24. Grosjean N. Maillet J.-M. Niccoli G., “On the Form Factors of Local Operators in the Bazhanov-Stroganov and Chiral Potts Models”, Ann. Henri Poincare, 16:5 (2015), 1103–1153  crossref  isi
    25. Stanislav Pakuliak, Eric Ragoucy, Nikita A. Slavnov, “$GL(3)$-Based Quantum Integrable Composite Models. I. Bethe Vectors”, SIGMA, 11 (2015), 063, 20 pp.  mathnet  crossref  mathscinet  elib
    26. N. M. Bogoliubov, “Time-dependent correlation functions for a bimodal Bose–Hubbard model”, J. Math. Sci. (N. Y.), 213:5 (2016), 662–670  mathnet  crossref  mathscinet
    27. Samuel Belliard, Rodrigo A. Pimenta, “Slavnov and Gaudin–Korepin Formulas for Models without $\mathrm{U}(1)$ Symmetry: the Twisted XXX Chain”, SIGMA, 11 (2015), 099, 12 pp.  mathnet  crossref
    28. Arthur Hutsalyuk, Andrii Liashyk, Stanislav Z. Pakuliak, Eric Ragoucy, Nikita A. Slavnov, “Multiple actions of the monodromy matrix in $\mathfrak{gl}(2|1)$-invariant integrable models”, SIGMA, 12 (2016), 099, 22 pp.  mathnet  crossref  mathscinet  elib
    29. Hutsalyuk A. Liashyk A. Pakuliak S.Z. Ragoucy E. Slavnov N.A., “Scalar products of Bethe vectors in models with ${\mathfrak{gl}}(2| 1)$ symmetry 1. Super-analog of Reshetikhin formula”, J. Phys. A-Math. Theor., 49:45 (2016), 454005, 1–28  crossref  mathscinet  isi  scopus
    30. Nepomechie R.I. Pimenta R.A., “Algebraic Bethe ansatz for the Temperley?Lieb spin-1 chain”, Nucl. Phys. B, 910 (2016), 885–909  crossref  mathscinet  zmath  isi  elib  scopus
    31. Nepomechie R.I. Pimenta R.A., “Universal Bethe ansatz solution for the Temperley–Lieb spin chain”, Nucl. Phys. B, 910 (2016), 910–928  crossref  mathscinet  zmath  isi  elib  scopus
    32. Kozlowski K.K. Ragoucy E., “Asymptotic behaviour of two-point functions in multi-species models”, Nucl. Phys. B, 906 (2016), 241–288  crossref  mathscinet  zmath  isi  elib  scopus
    33. A. A. Hutsalyuk, A. Liashyk, S. Z. Pakulyak, E. Ragoucy, N. A. Slavnov, “Current presentation for the super-Yangian double $DY(\mathfrak{gl}(m|n))$ and Bethe vectors”, Russian Math. Surveys, 72:1 (2017), 33–99  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    34. Hutsalyuk A. Liashyk A. Pakuliak S.Z. Ragoucy E. Slavnov N.A., “Scalar products of Bethe vectors in models with $\mathfrak{g}\mathfrak{l}(2|1)$ symmetry 2. Determinant representation”, J. Phys. A-Math. Theor., 50:3 (2017), 034004  crossref  mathscinet  zmath  isi  elib  scopus
    35. Goehmann F. Karbach M. Kluemper A. Kozlowski K.K. Suzuki J., “Thermal Form-Factor Approach to Dynamical Correlation Functions of Integrable Lattice Models”, J. Stat. Mech.-Theory Exp., 2017, 113106  crossref  isi
    36. Piroli L. Calabrese P., “Exact Dynamics Following An Interaction Quench in a One-Dimensional Anyonic Gas”, Phys. Rev. A, 96:2 (2017), 023611  crossref  isi
    37. James A.J.A. Konik R.M. Lecheminant Ph. Robinson N.J. Tsvelik A.M., “Non-Perturbative Methodologies For Low-Dimensional Strongly-Correlated Systems: From Non-Abelian Bosonization to Truncated Spectrum Methods”, Rep. Prog. Phys., 81:4 (2018), 046002  crossref  isi
    38. Hutsalyuk A. Liashyk A. Pakuliak S.Z. Ragoucy E. Slavnov N.A., “Scalar Products and Norm of Bethe Vectors For Integrable Models Based on U-Q ((Gl)Over-Cap(M))”, SciPost Phys., 4:1 (2018), 006  crossref  isi
    39. Bogoliubov N. Malyshev C., “The Phase Model and the Norm-Trace Generating Function of Plane Partitions”, J. Stat. Mech.-Theory Exp., 2018, 083101  crossref  isi
    40. Jules Lamers, “The Functional Method for the Domain-Wall Partition Function”, SIGMA, 14 (2018), 064, 23 pp.  mathnet  crossref
    41. Gromov N. Levkovich-Maslyuk F., “New Compact Construction of Eigenstates For Supersymmetric Spin Chains”, J. High Energy Phys., 2018, no. 9, 085  crossref  isi  scopus
    42. Belliard S. Slavnov N.A. Vallet B., “Scalar Product of Twisted Xxx Modified Bethe Vectors”, J. Stat. Mech.-Theory Exp., 2018, 093103  crossref  isi  scopus
    43. N. A. Slavnov, “Determinant representations for scalar products in the algebraic Bethe ansatz”, Theoret. and Math. Phys., 197:3 (2018), 1771–1778  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    44. Gerrard A. MacKay N. Regelskis V., “Nested Algebraic Bethe Ansatz For Open Spin Chains With Even Twisted Yangian Symmetry”, Ann. Henri Poincare, 20:2 (2019), 339–392  crossref  mathscinet  zmath  isi  scopus
    45. Samuel Belliard, Nikita A. Slavnov, “Scalar Products in Twisted XXX Spin Chain. Determinant Representation”, SIGMA, 15 (2019), 066, 30 pp.  mathnet  crossref  mathscinet
    46. N. A. Slavnov, “Generating function for scalar products in the algebraic Bethe ansatz”, Theoret. and Math. Phys., 204:3 (2020), 1216–1226  mathnet  crossref  crossref  mathscinet  isi  elib
    47. Piroli L. Scopa S. Calabrese P., “Determinant Formula For the Field Form Factor in the Anyonic Lieb-Liniger Model”, J. Phys. A-Math. Theor., 53:40 (2020), 405001  crossref  isi
    48. Garcia Juan Miguel Nieto Torrielli A., “Norms and Scalar Products For Ads(3)”, J. Phys. A-Math. Theor., 53:14 (2020), 145401  crossref  isi
    49. Litvinov A. Vilkoviskiy I., “Liouville Reflection Operator, Affine Yangian and Bethe Ansatz”, J. High Energy Phys., 2020, no. 12, 100  crossref  isi
    50. Sergey É. Derkachov, Karol K. Kozlowski, Alexander N. Manashov, “Completeness of SoV Representation for $\mathrm{SL}(2,\mathbb R)$ Spin Chains”, SIGMA, 17 (2021), 063, 26 pp.  mathnet  crossref
    51. S. Belliard, N. A. Slavnov, “Overlap between usual and modified Bethe vectors”, Theoret. and Math. Phys., 209:1 (2021), 1387–1402  mathnet  crossref  crossref  isi
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