Аннотация:
We consider the XXX spin-12 Heisenberg chain on the circle with an arbitrary twist. We characterize its spectral problem using the modified algebraic Bethe anstaz and study the scalar product between the Bethe vector and its dual. We obtain modified Slavnov and Gaudin–Korepin formulas for the model. Thus we provide a first example of such formulas for quantum integrable models without U(1) symmetry characterized by an inhomogenous Baxter T-Q equation.
Образец цитирования:
Samuel Belliard, Rodrigo A. Pimenta, “Slavnov and Gaudin–Korepin Formulas for Models without U(1) Symmetry: the Twisted XXX Chain”, SIGMA, 11 (2015), 099, 12 pp.
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\by Samuel~Belliard, Rodrigo~A.~Pimenta
\paper Slavnov and Gaudin--Korepin Formulas for Models without $\mathrm{U}(1)$~Symmetry: the Twisted XXX Chain
\jour SIGMA
\yr 2015
\vol 11
\papernumber 099
\totalpages 12
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\crossref{https://doi.org/10.3842/SIGMA.2015.099}
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Эта публикация цитируется в следующих 19 статьяx:
Samuel Belliard, Rodrigo Alves Pimenta, Nikita A. Slavnov, “Modified rational six vertex model on the rectangular lattice”, SciPost Phys., 16:1 (2024), 9–20
Giuliano Niccoli, Véronique Terras, “On correlation functions for the open XXZ chain with non-longitudinal boundary fields: The case with a constraint”, SciPost Phys., 16:4 (2024)
G Niccoli, V Terras, “Correlation functions for open XXZ spin 1/2 quantum chains with unparallel boundary magnetic fields”, J. Phys. A: Math. Theor., 55:40 (2022), 405203
С. Беллиард, Н. А. Славнов, “Перекрытие обычных и модифицированных векторов Бете”, ТМФ, 209:1 (2021), 82–100; S. Belliard, N. A. Slavnov, “Overlap between usual and modified Bethe vectors”, Theoret. and Math. Phys., 209:1 (2021), 1387–1402
Niccoli G. Pei H. Terras V., “Correlation Functions By Separation of Variables: the Xxx Spin Chain”, SciPost Phys., 10:1 (2021), 006
Belliard S. Pimenta R.A. Slavnov N.A., “Scalar Product For the Xxz Spin Chain With General Integrable Boundaries”, J. Phys. A-Math. Theor., 54:34 (2021), 344001
Y. Qiao, Zh. Xin, X. Xu, K. Hao, T. Yang, J. Cao, W.-L. Yang, “Correlation functions of the xxz spin chain with the twisted boundary condition”, J. Math. Phys., 61:3 (2020), 033502
N. Slavnov, A. Zabrodin, A. Zotov, “Scalar products of Bethe vectors in the 8-vertex model”, J. High Energy Phys., 2020, no. 6
Samuel Belliard, Nikita A. Slavnov, “Scalar Products in Twisted XXX Spin Chain. Determinant Representation”, SIGMA, 15 (2019), 066, 30 pp.
S. Belliard, N. A. Slavnov, “Why scalar products in the algebraic Bethe ansatz have determinant representation”, J. High Energy Phys., 2019, no. 10, 103
P. Baseilhac, R. A. Pimenta, “Diagonalization of the Heun-Askey-Wilson operator, leonard pairs and the algebraic Bethe ansatz”, Nucl. Phys. B, 949 (2019), 114824
S. Belliard, N. A. Slavnov, “A note on gl2-invariant Bethe vectors”, J. High Energy Phys., 2018, no. 4, 031
S. Belliard, A. Faribault, “Ground state solutions of inhomogeneous Bethe equations”, SciPost Phys., 4:6 (2018), 030
Samuel Belliard, Nikita A. Slavnov, Benoit Vallet, “Modified Algebraic Bethe Ansatz: Twisted XXX Case”, SIGMA, 14 (2018), 054, 18 pp.
S. Belliard, N. A. Slavnov, B. Vallet, “Scalar product of twisted XXX modified Bethe vectors”, J. Stat. Mech.-Theory Exp., 2018, 093103
S. Belliard, N. A. Slavnov, “A note on gl2-invariant Bethe vectors”, JHEP, 2018 (2018), 31–14
Nicolas Crampe, “Algebraic Bethe Ansatz for the XXZ Gaudin Models with Generic Boundary”, SIGMA, 13 (2017), 094, 13 pp.
A. Faribault, H. Tschirhart, “Common framework and quadratic Bethe equations for rational Gaudin magnets in arbitrarily oriented magnetic fields”, SciPost Phys., 3:2 (2017), UNSP 009
S. Belliard, R. A. Pimenta, “Slavnov and Gaudin–Korepin formulas for models without U(1) symmetry: the XXX chain on the segment”, J. Phys. A-Math. Theor., 49:17 (2016), 17LT01
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