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Related papers: Lectures on the Bethe Ansatz

200 papers

We consider the Bethe ansatz solution of integrable models interacting through factorized $S$-matrices based on the central extention of the $\bf{su}(2|2)$ symmetry. The respective $\bf{su}(2|2)$ $R$-matrix is explicitly related to that of…

High Energy Physics - Theory · Physics 2008-11-26 M. J. Martins , C. S. Melo

We continue the survey initiated in arXiv:2012.14197 to explore the Bethe/Gauge correspondence between supersymmetric SO/Sp gauge theories in 2d/3d/4d and open spin chain with integrable boundaries. We collect the known Bethe ansatz…

High Energy Physics - Theory · Physics 2024-10-01 Ziwei Wang , Rui-Dong Zhu

We consider the finite volume mean values of current operators in integrable spin chains with local interactions, and provide an alternative derivation of the exact result found recently by the author and two collaborators. We use a certain…

Statistical Mechanics · Physics 2020-02-05 Balázs Pozsgay

The off-diagonal Bethe ansatz method is generalized to the integrable model associated with the $sp(4)$ (or $C_2$) Lie algebra. By using the fusion technique, we obtain the complete operator product identities among the fused transfer…

Mathematical Physics · Physics 2019-06-05 Guang-Liang Li , Junpeng Cao , Panpan Xue , Zhi-Rong Xin , Kun Hao , Wen-Li Yang , Kangjie Shi , Yupeng Wang

We present in an unified and detailed way the nested Bethe ansatz for open spin chains based on Y(gl(\fn)), Y(gl(\fm|\fn)), U_{q}(gl(\fn)) or U_{q}(gl(\fm|\fn)) (super)algebras, with arbitrary representations (i.e. `spins') on each site of…

Mathematical Physics · Physics 2015-05-13 S. Belliard , E. Ragoucy

The integrable close and open chain models can be formulated in terms of generators of the Hecke algebras. In this review paper, we describe in detail the Bethe ansatz for the XXX and the XXZ integrable close chain models. We find the Bethe…

Mathematical Physics · Physics 2015-07-02 C. Burdik , J. Fuksa , A. P. Isaev , S. O. Krivonos , O. Navratil

We propose a one-dimensional model of spinor bosons with SU(2) symmetry and a two-body finite range Gaussian interaction potential. We show that the model is exactly solvable when the width of the interaction potential is much smaller…

Statistical Mechanics · Physics 2012-01-25 J. Y. Lee , X. W. Guan , A. del Campo , M. T. Batchelor

We consider quantum quenches in the integrable $SU(3)$-invariant spin chain (Lai-Sutherland model) which admits a Bethe ansatz description in terms of two different quasiparticle species, providing a prototypical example of a model solvable…

Statistical Mechanics · Physics 2019-06-20 Lorenzo Piroli , Eric Vernier , Pasquale Calabrese , Balázs Pozsgay

Exact solutions of quantum lattice models serve as useful guides for interpreting physical phenomena in condensed matter systems. Prominent examples of integrability appear in one dimension, including the Heisenberg chain, where the Bethe…

Strongly Correlated Electrons · Physics 2025-01-27 Ronald Melendrez , Bhaskar Mukherjee , Marcin Szyniszewski , Christopher J. Turner , Arijeet Pal , Hitesh J. Changlani

We study SU(3)-invariant integrable models solvable by nested algebraic Bethe ansatz. We obtain a determinant representation for particular case of scalar products of Bethe vectors. This representation can be used for the calculation of…

Mathematical Physics · Physics 2015-09-07 S. Belliard , S. Pakuliak , E. Ragoucy , N. A. Slavnov

In this proceeding we present the nested Bethe ansatz for open spin chains of XXX-type, with arbitrary representations (i.e. `spins') on each site of the chain and diagonal boundary matrices $(K^+(u),K^-(u))$. The nested Bethe anstaz…

Mathematical Physics · Physics 2012-06-28 S. Belliard , E. Ragoucy

A generalization of the eight vertex model by means of higher spin representations of the Sklyanin algebra is investigated by the quantum inverse scattering method and the algebraic Bethe Ansatz. Under the well-known string hypothesis…

q-alg · Mathematics 2009-10-28 Takashi Takebe

We study the trigonometric quantum spin-Calogero-Sutherland model, and the Haldane-Shastry spin chain as a special case, using a Bethe-ansatz analysis. We harness the model's Yangian symmetry to import the standard tools of integrability…

Mathematical Physics · Physics 2025-03-27 Gwenaël Ferrando , Jules Lamers , Fedor Levkovich-Maslyuk , Didina Serban

We present a global treatment of the analytical Bethe ansatz for gl(N) spin chains admitting on each site an arbitrary representation. The method applies for closed and open spin chains, and also to the case of soliton non-preserving…

Mathematical Physics · Physics 2015-06-26 D. Arnaudon , N. Crampe , A. Doikou , L. Frappat , Eric Ragoucy

The Bethe ansatz for the one-dimensional s=1/2 Heisenberg ferromagnet is introduced at an elementary level. The presentation follows Bethe's original work very closely. A detailed description and a complete classification of all two-magnon…

Statistical Mechanics · Physics 2007-05-23 Michael Karbach , Gerhard Muller

Using the algebraic Bethe ansatz method, and the solution of the quantum inverse scattering problem for local spins, we obtain multiple integral representations of the $n$-point correlation functions of the XXZ Heisenberg spin-$1 \over 2$…

Mathematical Physics · Physics 2018-08-30 N. Kitanine , J. M. Maillet , V. Terras

This paper is a review of the works devoted to understanding and reinterpretation of the theory of quantum integrable models solvable by Bethe ansatz in terms of the theory of purely classical soliton equations. Remarkably, studying…

Mathematical Physics · Physics 2025-03-19 A. Zabrodin

We investigate the integrable structure of spin chain models with centrally extended su(2|2) and psu(2,2|4) symmetry. These chains have their origin in the planar AdS/CFT correspondence, but they also contain the one-dimensional Hubbard…

Exactly Solvable and Integrable Systems · Physics 2011-02-16 Niklas Beisert

In this paper and upcoming ones, we initiate a systematic study of Bethe ansatz equations for integrable models by modern computational algebraic geometry. We show that algebraic geometry provides a natural mathematical language and…

High Energy Physics - Theory · Physics 2018-04-18 Yunfeng Jiang , Yang Zhang

We argue that the recently discovered integrability in the large-N CFT/AdS system is equivalent to diffractionless scattering of the corresponding hidden elementary excitations. This suggests that, perhaps, the key tool for finding the…

High Energy Physics - Theory · Physics 2009-11-10 Matthias Staudacher