Boosting nearest-neighbour to long-range integrable spin chains

Journal of Statistical Mechanics: Theory and Experiment

Volumn 2008, Issue 11, 2008, Pages

  Bargheer, Till ^a   Beisert, Niklas ^a   Loebbert, Florian ^a  

^a ALBERT EINSTEIN INSTITUT   (Germany)

Author keywords

Integrable spin chains (vertex models); Ladders and planes (theory); Quantum integrability (Bethe ansatz); Spin chains

Indexed keywords

EID: 65549110630     PISSN: 17425468     EISSN: 17425468     Source Type: Journal    
DOI: 10.1088/1742-5468/2008/11/L11001     Document Type: Article

References (26)

1. Bethe H 1931 Zur Theorie der Metalle I. Eigenwerte und Eigenfunktionen der linearen Atomkette Z. Phys. 71 205
2. Heisenberg W 1928 Zur Theorie des Ferromagnetismus Z. Phys. 49 619
3. 2 exchange Phys. Rev. Lett. 60 635
4. Shastry B S 1988 Exact solution of an S = 1/2 Heisenberg antiferromagnetic chain with long ranged interactions Phys. Rev. Lett. 60 639
5. Inozemtsev V I 1990 On the connection between the one-dimensional s = 1/2 Heisenberg chain and Haldane Shastry model J. Stat. Phys. 59 1143
6. Inozemtsev V I 2003 Integrable Heisenberg-van Vleck chains with variable range exchange Phys. Part. Nucl. 34 166 [arXiv:hep-th/0201001] (Pubitemid 36446205)
7. Minahan J A and Zarembo K 2003 The Bethe-ansatz for super Yang-Mills J. High Energy Phys. JHEP03(2003)013 [arXiv:hep-th/0212208] (Pubitemid 41072699)
8. Beisert N, Kristjansen C and Staudacher M 2003 The dilatation operator of conformal super Yang-Mills theory Nucl. Phys. B 664 131 [arXiv:hep-th/0303060] (Pubitemid 36860529)
9. Beisert N and Staudacher M 2003 The SYM integrable super spin chain Nucl. Phys. B 670 439 [arXiv:hep-th/0307042] (Pubitemid 37223521)
10. Beisert N 2004 The dilatation operator of super Yang-Mills theory and integrability Phys. Rep. 405 1 [arXiv:hep-th/0407277] (Pubitemid 40013937)
11. Beisert N and Klose T 2006 Long-range GL(n) integrable spin chains and plane-wave matrix theory J. Stat. Mech. P07006 [arXiv:hep-th/0510124]
12. Serban D and Staudacher M 2004 Planar gauge theory and the Inozemtsev long range spin chain J. High Energy Phys. JHEP06(2004)001 [arXiv:hep-th/ 0401057] (Pubitemid 41071965)
13. Beisert N and Erkal D 2008 Yangian symmetry of long-range gl(N) integrable spin chains J. Stat. Mech. P03001 [arXiv:0711.4813]
14. Sogo K and Wadati M 1983 Boost operator and its application to quantum Gelfand-Levitan equation for Heisenberg-Ising chain with spin one-half Prog. Theor. Phys. 69 431
15. Beisert N, Dippel V and Staudacher M 2004 A novel long range spin chain and planar super Yang-Mills J. High Energy Phys. JHEP07(2004)075 [arXiv:hep-th/0405001] (Pubitemid 41071957)
16. Arutyunov G, Frolov S and Staudacher M 2004 Bethe ansatz for quantum strings J. High Energy Phys. JHEP10(2004)016 [arXiv:hep-th/0406256] (Pubitemid 41071687)
17. Reshetikhin N Y 1983 A method of functional equations in the theory of exactly solvable quantum system Lett. Math. Phys. 7 205
18. Reshetikhin N Y 1985 Integrable models of quantum one-dimensional magnets with O(N) and Sp(2K) symmetry Theor. Math. Phys. 63 555
19. Ogievetsky E and Wiegmann P 1986 Factorized S matrix and the Bethe ansatz for simple Lie groups Phys. Lett. B 168 360
20. Sutherland B 1978 A brief history of the quantum soliton with new results on the quantization of the Toda lattice Rocky Mtn. J. Math. 8 413
21. Bargheer T, Beisert N and Loebbert F Long-range integrable spin chains by algebra-preserving deformations in progress
22. Minahan J A and Zarembo K 2008 The Bethe ansatz for superconformal Chern-Simons arXiv:0806.3951
23. Bak D and Rey S-J 2008 Integrable spin chain in superconformal Chern-Simons theory arXiv:0807.2063
24. Aharony O, Bergman O, Jafferis D L and Maldacena J 2008 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals arXiv:0806.1218
25. Beisert N and Loebbert F 2008 Open perturbatively long-range integrable gl(N) spin chains arXiv:0805.3260
26. Zwiebel B I 2008 Iterative structure of the SYM spin chain arXiv:0806.1786