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Algebra i Analiz, 2005, Volume 17, Issue 1, Pages 115–159 (Mi aa648)  

This article is cited in 27 scientific papers (total in 27 papers)

Research Papers

A recursion formula for the correlation functions of an inhomogeneous $XXX$ model

H. Boosab, M. Jimboc, T. Miwad, F. Smirnove, Y. Takeyamaf

a Institute for High Energy Physics, Protvino, Russia
b Physics Department University of Wuppertal, Germany
c Graduate School of Mathematical Sciences, the University of Tokyo, Japan
d Department of Mathematics, Graduate School of Science, Kyoto University, Japan
e (Membre du CNRS), Laboratoire de Physique Théorique, et Hautes Energies Université Pierre et Marie Curie, Paris, France
f Graduate School of Pure and Applied Sciences, University of Tsukuba, Japan

Abstract: A new recursion formula is presented for the correlation functions of the integrable spin $1/2 XXX$ chain with inhomogeneity. It links the correlators involving $n$ consecutive lattice sites to those with $n-1$ and $n-2$ sites. In a series of papers by V. Korepin and two of the present authors, it was discovered that the correlators have a certain specific structure as functions of the inhomogeneity parameters. The formula mentioned above makes it possible to prove this structure directly, as well as to obtain an exact description of the rational functions that were left undetermined in the earlier work.

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English version:
St. Petersburg Mathematical Journal, 2006, 17:1, 85–117

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Received: 09.10.2004

Citation: H. Boos, M. Jimbo, T. Miwa, F. Smirnov, Y. Takeyama, “A recursion formula for the correlation functions of an inhomogeneous $XXX$ model”, Algebra i Analiz, 17:1 (2005), 115–159; St. Petersburg Math. J., 17:1 (2006), 85–117

Citation in format AMSBIB
\by H. Boos, M. Jimbo, T. Miwa, F. Smirnov, Y. Takeyama
\paper A~recursion formula for the correlation functions of an inhomogeneous $XXX$ model
\jour Algebra i Analiz
\yr 2005
\vol 17
\issue 1
\pages 115--159
\jour St. Petersburg Math. J.
\yr 2006
\vol 17
\issue 1
\pages 85--117

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    This publication is cited in the following articles:
    1. Boos H., Jimbo M., Miwa T., Smirnov F., Takeyama Y., “Traces on the Sklyanin algebra and correlation functions of the eight-vertex model”, J. Phys. A, 38:35 (2005), 7629–7659  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    2. Boos H. E., Göhmann F., Klümper A., Suzuki J., “Factorization of multiple integrals representing the density matrix of a finite segment of the Heisenberg spin chain”, J. Stat. Mech., 2006, P04001  crossref  isi  elib  scopus
    3. Boos H., Jimbo M., Miwa T., Smirnov F., Takeyama Y., “Density matrix of a finite sub-chain of the Heisenberg anti-ferromagnet”, Lett. Math. Phys., 75:3 (2006), 201–208  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    4. Boos H., Jimbo M., Miwa T., Smirnov F., Takeyama Y., “Reduced qKZ equation and correlation functions of the XXZ model”, Comm. Math. Phys., 261:1 (2006), 245–276  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    5. Sato J., Shiroishi M., Takahashi M., “Exact evaluation of density matrix elements for the Heisenberg chain”, J. Stat. Mech., 2006, P12017  crossref  isi  elib  scopus
    6. Boos H., Jimbo M., Miwa T., Smirnov F., Takeyama Y., “Algebraic representation of correlation functions in integrable spin chains”, Ann. Henri Poincaré, 7:7–8 (2006), 1395–1428  crossref  mathscinet  zmath  adsnasa  isi  scopus
    7. Korff C., “A $Q$-operator for the twisted $XXX$ model”, J. Phys. A, 39:13 (2006), 3203–3219  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    8. Sato J., Shiroishi M., “Density matrix elements and entanglement entropy for the spin-1/2 $XXZ$ chain at $\Delta=1/2$”, J. Phys. A, 40:30 (2007), 8739–8749  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    9. Boos H. E., Göhmann F., Klümper A., Suzuki J., “Factorization of the finite temperature correlation functions of the $XXZ$ chain in a magnetic field”, J. Phys. A, 40:35 (2007), 10699–10727  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    10. Castro-Alvaredo O. A., Maillet J. M., “Form factors of integrable Heisenberg (higher) spin chains”, J. Phys. A, 40:27 (2007), 7451–7471  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    11. Damerau J., Göhmann F., Hasenclever N. P., Klümper A., “Density matrices for finite segments of Heisenberg chains of arbitrary length”, J. Phys. A, 40:17 (2007), 4439–4453  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    12. Bortz M., Sato J., Shiroishi M., “String correlation functions of the spin-1/2 Heisenberg $XXZ$ chain”, J. Phys. A, 40:16 (2007), 4253–4271  crossref  mathscinet  zmath  adsnasa  isi  elib
    13. Boos H., Jimbo M., Miwa T., Smirnov F., Takeyama Y., “Hidden Grassmann structure in the $XXZ$ model”, Comm. Math. Phys., 272:1 (2007), 263–281  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    14. Maillet J.-M., “Heisenberg spin chains: From quantum groups to neutron scattering experiments”, Quantum Spaces: Poincare Seminar 2007, Progress in Mathematics, 53, 2007, 161–201  crossref  mathscinet  zmath  adsnasa  isi
    15. Boos H., Göhmann F., “On the physical part of the factorized correlation functions of the $XXZ$ chain”, J. Phys. A, 42:31 (2009), 315001, 27 pp.  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    16. Minoru Takahashi, “Correlation Function and Simplified TBA Equations for XXZ Chain”, SIGMA, 7 (2011), 004, 15 pp.  mathnet  crossref  mathscinet
    17. 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  crossref  isi  scopus
    18. Sato J., Aufgebauer B., Boos H., Goehmann F., Kluemper A., Takahashi M., Trippe Ch., “Computation of Static Heisenberg-Chain Correlators: Control over Length and Temperature Dependence”, Physical Review Letters, 106:25 (2011), 257201  crossref  adsnasa  isi  elib  scopus
    19. Aufgebauer B., Kluemper A., “Finite Temperature Correlation Functions From Discrete Functional Equations”, J. Phys. A-Math. Theor., 45:34 (2012), 345203  crossref  mathscinet  zmath  isi  elib  scopus
    20. Levy-Bencheton D., Terras V., “An Algebraic Bethe Ansatz Approach to Form Factors and Correlation Functions of the Cyclic Eight-Vertex Solid-on-Solid Model”, J. Stat. Mech.-Theory Exp., 2013, P04015  crossref  mathscinet  isi  elib  scopus
    21. M. Jimbo, T. Miwa, F. A. Smirnov, “Creation operators for the Fateev–Zamolodchikov spin chain”, Theoret. and Math. Phys., 181:1 (2014), 1169–1193  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib  elib
    22. Boos H., Goehmann F., Kluemper A., Nirov Kh.S., Razumov A.V., “Universal R-Matrix and Functional Relations”, Rev. Math. Phys., 26:6 (2014), 1430005  crossref  mathscinet  zmath  isi  elib  scopus
    23. Ribeiro G.A.P., Kluemper A., “Correlation functions of the integrable spin- s chain”, J. Phys. A-Math. Theor., 49:25 (2016), 254001  crossref  mathscinet  zmath  isi  elib  scopus
    24. Pozsgay B., “Excited state correlations of the finite Heisenberg chain”, J. Phys. A-Math. Theor., 50:7 (2017), 074006  crossref  mathscinet  zmath  isi  scopus
    25. Boos H., Hutsalyuk A., Nirov Kh.S., “On the Calculation of the Correlation Functions of the Sl(3)-Model By Means of the Reduced Qkz Equation”, J. Phys. A-Math. Theor., 51:44 (2018), 445202  crossref  isi  scopus
    26. Miwa T., Smirnov F., “New Exact Results on Density Matrix For Xxx Spin Chain”, Lett. Math. Phys., 109:3 (2019), 675–698  crossref  mathscinet  zmath  isi  scopus
    27. Ribeiro G.A.P., Kluemper A., “Correlation Functions of the Integrable Su (N) Spin Chain”, J. Stat. Mech.-Theory Exp., 2019, 013103  crossref  mathscinet  isi  scopus
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