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Quantum Integrable 1D anyonic Models: Construction through Braided Yang-Baxter Equation [PDF]
Symmetry, Integrability and Geometry: Methods and Applications, 2010 Applying braided Yang-Baxter equation quantum integrable and Bethe ansatz solvable 1D anyonic lattice and field models are constructed. Along with known models we discover novel lattice anyonic and $q$-anyonic models as well as nonlinear Schr\"odinger ...
Kundu, Anjan
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Solution of tetrahedron equation and cluster algebras
Journal of High Energy Physics, 2021 We notice a remarkable connection between the Bazhanov-Sergeev solution of Zamolodchikov tetrahedron equation and certain well-known cluster algebra expression. The tetrahedron transformation is then identified with a sequence of four mutations.
P. Gavrylenko +2 more
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Flag integrable models and generalized graded algebras
Journal of High Energy Physics, 2023 We introduce new classes of integrable models that exhibit a structure similar to that of flag vector spaces. We present their Hamiltonians, R-matrices and Bethe-ansatz solutions. These models have a new type of generalized graded algebra symmetry.
Marius de Leeuw +2 more
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Journal of High Energy Physics, 2020 We present a general formula for constructing R-matrices with non-additive spectral parameters associated with a type-I quantum superalgebra. The spectral parameters originate from two one-parameter families of inequivalent finite-dimensional irreducible
Yao-Zhong Zhang, Jason L. Werry
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Duality relations for overlaps of integrable boundary states in AdS/dCFT
Journal of High Energy Physics, 2021 The encoding of all possible sets of Bethe equations for a spin chain with SU(N|M) symmetry into a QQ-system calls for an expression of spin chain overlaps entirely in terms of Q-functions.
Charlotte Kristjansen +2 more
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On Bethe vectors in gl3 $$ \mathfrak{g}{\mathfrak{l}}_3 $$-invariant integrable models
Journal of High Energy Physics, 2018 We consider quantum integrable models solvable by the nested algebraic Bethe ansatz and possessing gl3 $$ \mathfrak{g}{\mathfrak{l}}_3 $$-invariant R-matrix.
A. Liashyk, N. A. Slavnov
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Spectrum of the quantum integrable D 2 2 $$ {D}_2^{(2)} $$ spin chain with generic boundary fields
Journal of High Energy Physics, 2022 Exact solution of the quantum integrable D 2 2 $$ {D}_2^{(2)} $$ spin chain with generic integrable boundary fields is constructed. It is found that the transfer matrix of this model can be factorized as the product of those of two open staggered ...
Guang-Liang Li +4 more
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Why scalar products in the algebraic Bethe ansatz have determinant representation
Journal of High Energy Physics, 2019 We show that the scalar products of on-shell and off-shell Bethe vectors in the algebralic Bethe ansatz solvable models satisfy a system of linear equations. We find solutions to this system for a wide class of integrable models. We also apply our method
S. Belliard, N. A. Slavnov
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Journal of High Energy Physics, 2020 Based on its off-diagonal Bethe ansatz solution, we study the thermodynamic limit of the spin- 1 2 $$ \frac{1}{2} $$ XYZ spin chain with the antiperiodic boundary condition.
Zhirong Xin +5 more
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Journal of High Energy Physics, 2020 We formulate Q-systems for the closed XXZ, open XXX and open quantum- group-invariant XXZ quantum spin chains. Polynomial solutions of these Q-systems can be found efficiently, which in turn lead directly to the admissible solutions of the corresponding ...
Zoltán Bajnok +3 more
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