The analytic Bethe ansatz for a chain with centrally extended symmetry
By N. Beisert. 2006
174 citations recorded by the source corpus.
We investigate the integrable structure of spin chain models with centrally extended and symmetry. These chains have their origin in the planar anti-de Sitter/conformal field theory correspondence, but they also contain the one-dimensional Hubbard model as a special case. We begin with an overview of the representation theory of centrally extended . These results are applied in the construction and investigation of an interesting S-matrix with symmetry. In particular, they enable a remarkably simple proof of the Yang–Baxter relation. We also show the equivalence of the S-matrix to Shastry’s R-matrix and thus uncover a hidden supersymmetry in the integrable structure of the Hubbard model. We then construct eigenvalues of the corresponding transfer matrix in order to formulate an analytic Bethe ansatz. Finally, the form of transfer matrix eigenvalues for models with symmetry is sketched.
Subfields: Geometry and Topology, Nuclear and High Energy Physics, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/924a5c4e3fb53d20edb3fe2d46dd4fc90e5db36c
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In Geometry and Topology
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Citations in the corpus
- Quantum deformations of the one-dimensional Hubbard model (2008, methodology): “f two fundamental representations (2.36) h0,0i⊗ h0,0i = {0,0}. (3.2) We present our findings for the ten functions in Tab. 2. This derivation parallels completely the case of the undeformed algebra in [17] and for q= 1 the results agree. Note that C 12 = F 12 and H 12 = K 12 if γis determined by (2.6”
- Transcendentality and crossing (2006, background): “degeneration of the complex tori defining the kinematical space for the bound states in [40, 41 ].”
- String hypothesis for the AdS5 × S5 mirror (2009, methodology): “modynamic limit. We use the Bethe-Yang equations of [16] and the fusion procedure, see e.g. [44], to write down the equations for the complete spectrum of the mirror theory. We use the observation of [31] that the equations for auxiliary roots can be interpreted as the Lieb-Wu equations for an inhom”