Review of AdS/CFT Integrability, Chapter I.3: Long-Range Spin Chains

Rej, Adam

doi:10.1007/s11005-011-0509-6

Cited by 15 publications

(19 citation statements)

References 41 publications

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“…The infinite volume scattering description of theory can be found in chapters [10,11]. The ABA equations for the planar AdS/CFT model was conjectured in [12] (and thoroughly discussed in chapters [13,14]), while the analogous ABA for the mirror model was described in [15]. As the color structure (su(2|2)) of the scattering matrix is the same as that of the Hubbard model, the Hubbard TBA solution can be adopted [16].…”

Section: Guide To the Literaturementioning

confidence: 99%

Review of AdS/CFT Integrability, Chapter III.6: Thermodynamic Bethe Ansatz

Bajnok

2011

Lett Math Phys

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Section: Guide To the Literaturementioning

confidence: 99%

Review of AdS/CFT Integrability, Chapter III.6: Thermodynamic Bethe Ansatz

Bajnok

2011

Lett Math Phys

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“…In particular, this type of systems have appeared as paradigms of various condensed matter systems exhibiting generalized exclusion statistics [15][16][17], the quantum Hall effect [18], and quantum electric transport phenomena [19,20]. More recently, quantum integrable spin chains with long-range interactions have played a key role in calculating higher-loop effects in the spectra of trace operators of planar N = 4 super Yang-Mills theory [21][22][23][24]. In the mathematics literature, this type of systems has been found to be relevant in different fields such as random matrix theory [25], multivariate orthogonal polynomials and Dunkl operators [26][27][28][29], and Yangian quantum groups [30][31][32][33].…”

Section: Introductionmentioning

confidence: 99%

The exactly solvable spin Sutherland model of type and its related spin chain

Basu-Mallick¹,

Finkel²,

González‐López³

2013

Nuclear Physics B

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We compute the spectrum of the su(m) spin Sutherland model of B N type, including the exact degeneracy of all energy levels. By studying the large coupling constant limit of this model and of its scalar counterpart, we evaluate the partition function of their associated spin chain of Haldane-Shastry type in closed form. With the help of the formula for the partition function thus obtained we study the chain's spectrum, showing that it cannot be obtained as a limiting case of its BC N counterpart. The structure of the partition function also suggests that the spectrum of the Haldane-Shastry spin chain of B N type is equivalent to that of a suitable vertex model, as is the case for its A N−1 counterpart, and that the density of its eigenvalues is normally distributed when the number of sites N tends to infinity. We analyze this last conjecture numerically using again the explicit formula for the partition function, and check its validity for several values of N and m.

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“…Perturbative corrections to the Yangian charges in subsectors have been studied in [32][33][34][35][36]. The integrable structure of spin-chains with long-range (LR) interactions, like the one emerging from gauge perturbation theory, lies outside the established picture [37], but a large class of LR spin-chains has been shown to display Yangian symmetries, see also [38][39][40][41]. In absence of other standard tools, Yangian symmetry provides a formal proof of integrability order by order in perturbation theory.…”

Section: Yangiansmentioning

confidence: 99%