Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Communications in Theoretical Physics

Yang-Baxterization of Spin-1 L Operator

Mo‐Lin Ge, Xu‐Feng Liu

Published Jul 1, 1992• 1 citation
Publisher

Abstract

The Yang-Baxterization of L operator is performed for spin-1 model, namely, for given braid group representation (BGR) the x -dependent L ( x ) operator can be determined where x is the spectral parameter. It is pointed out that in order to establish such an x -dependence besides the usual L ± operators in accordance with the Faddeev-Reshetikhin-Takhtajan (FRT) approach an additional operator L 0 should be introduced. The explicit expression of L 0 is given. This Yang-Baxterization prescription preserves the FRT and the YBE is satisfied by L ( x ) and R ( x ).

DOI
10.1088/0253-6102/18/1/59

Related papers

New R(x) -Matrix, L(x) -Operator and Quantum Algebra in Spin Model

Mo‐Lin Ge, Xu‐Feng Liu, Kang Xue

New solution of Yang-Bax ter equation for spin-1 ⊗ spin- tensorial space is derived based on the direct calculation and extended Yang-Baxterization prescription. It contains the standard solution as a special case. By employing Faddeev-Reshetikhin-Takhtajan approach we give the correspondent quantum algebraic structure. The Yang-Baxterization of the L -operator is also made explicitly.

Communications in Theoretical Physics•Sep 1, 1991•0 citations

Yang-Baxterization of the eight-vertex model: the braid group approach

Mo -L Ge, Leh-Hun Gwa, Hong-K Zhao

The braid group representation (BGR) for the eight-vertex model is solved for the case in which the total spins are not conserved. A Yang-Baxterization scheme is applied to obtain from these BGR the spectral-dependent solution; they are found to correspond to the free-fermion and the disorder-point solutions.

Journal of Physics A Mathematical and General•Aug 21, 1990•6 citations

Algebraic aspect and construction of Lax operators in quantum integrable systems

B Basu-mallick, Anjan Kundu

An algebraic construction more general and intimately connected with that of Faddeev1, along with its application for generating different classes of quantum integrable models are summarised to complement the recent results of ref. 1 ( L.D. Faddeev, Int. J. Mod. Phys. A10, 1845 (1995)). 1 A significant portion of an excellent recent review by Faddeev 1 is devoted to an important result showing deep relation between the Yang–Baxter equation and the quantum group. We are delighted to note that a scheme for systematic construction of the Lax operators through Yang–Baxterisation of the Faddeev–Reshetikhin–Takhtajan (FRT) algebra persued by us over the last few years 2,3 has an intimate connection with this approach. In fact our formulation gives a more general framework allowing construction of a wide range of Lax operators of lattice models and recovers the corresponding result of ref 1 related to Uqsl(2) as a particular case. Another convincing demonstration of the usefulness of our approach is that, the well known Lax operator of the lattice Liouville model 4 as well as the recently discovered 5 nontrivial spectral parameter dependent variant of it can be constructed directly and easily from our general form,

•Jan 1, 1995•1 citation

The Yang-Baxter Equation for the Chiral Potts Model and Integrable Parafermions

Zhao Zhang

A new type of Yang-Baxter equation (YBE) for $R$-operators depending on three spectral parameters is constructed from the star-triangle relation for the chiral Potts model. As the $Z_N$ symmetric generalization to the Ising model, its Boltzmann weights are known to depend on two variables describing a curve with genus larger than one for $N>2$, except for the self-dual point corresponding to the Fateev-Zamolodchikov chain. Combined with the fact that quantum Hamiltonians of edge-type models such as the Ising model contain both nearest-neighbor interaction and onsite potential terms, this leads naturally to an additional spectral parameter in the associated $R$-operator. The construction extends the edge-vertex correspondence of solvable lattice models, and provides a bridge between the Bazhanov-Stroganov four-parameter $R$-matrix---realized as an intertwiner of cyclic representations of $U_q(\mathfrak{sl}_2)$ at a root of unity---and Shastry's two-parameter $R$-operator obtained from the decorated YBE.

math-phCross-listedarXiv:2606.11146•Jun 10, 2026•0 citations

New type of solutions of Yang-Baxter equations, quantum entanglement and related physical models

Li-Wei Yu, Mo-Lin Ge

Starting from the Kauffman-Lomonaco braiding matrix transforming the natural basis to Bell states, the spectral parameter describing the entanglement is introduced through Yang-Baxterization. It gives rise to a new type of solutions for Yang-Baxter equation, called the type-II that differs from the familiar solution called type-I of YBE associated with the usual chain models. The Majorana fermionic version of type-II yields the Kitaev Hamiltonian. The introduced ℓ 1 -norm leads to the maximum of the entanglement by taking the extreme value and shows that it is related to the Wigner's D-function. Based on the Yang-Baxter equation the 3-body S-Matrix for type-II is explicitly given. Different from the type-I solution, the type-II solution of YBE should be considered in describing quantum information. The idea is further extended to 3 parafermion model based on SU (3) principal representation. The type-II is in difference from the familiar type-I in many respects. For example, the quantities corresponding to velocity in the chain models obey the Lorentzian additivity rather than Galilean rule ( u + v ). Most possibly, for the type-II solutions of YBE there may not exist RTT relation. Further more, for 3 parafermion model we only need the rational Yang-Baxterization, which seems like trigonometric. Similar discussions are also made in terms of generalized Yang-Baxter equation with three spin spaces .

arXiv:1810.09813•Journal of Physics Conference Series•Apr 1, 2019•2 citations

New spectral-parameter dependent solutions of the Yang-Baxter equation

Alexander. S. Garkun, Suvendu Barik, Aleksey K. Fedorov +1 more

The Yang-Baxter Equation (YBE) plays a crucial role for studying integrable many-body quantum systems. Many known YBE solutions provide various examples ranging from quantum spin chains to superconducting systems. Models of solvable statistical mechanics and their avatars are also based on YBE. Therefore, new solutions of the YBE could be used to construct new interesting 1D quantum or 2D classical systems with many other far-reaching applications. In this work, we attempt to find (almost) exhaustive set of solutions for the YBE in the lowest dimensions corresponding to a two-qubit case. We develop an algorithm, which can potentially be used for generating new higher-dimensional solutions of the YBE.

arXiv:2401.12710•Jan 23, 2024•3 citations
The Yang-Baxterization of L operator is performed for spin-1 model, namely, for given braid group representation (BGR) the x -dependent L ( x ) operator can be determined where x is the spectral parameter. It is pointed out that in order to establish such an x -dependence besides the usual L ± operators in accordance with the Faddeev-Reshetikhin-Takhtajan (FRT) approach an additional operator L 0 should be introduced. The explicit expression of L 0 is given. This Yang-Baxterization prescription preserves the FRT and the YBE is satisfied by L ( x ) and R ( x ).
An algebraic construction more general and intimately connected with that of Faddeev1, along with its application for generating different classes of quantum integrable models are summarised to complement the recent results of ref. 1 ( L.D. Faddeev, Int. J. Mod. Phys. A10, 1845 (1995)). 1 A significant portion of an excellent recent review by Faddeev 1 is devoted to an important result showing deep relation between the Yang–Baxter equation and the quantum group. We are delighted to note that a scheme for systematic construction of the Lax operators through Yang–Baxterisation of the Faddeev–Reshetikhin–Takhtajan (FRT) algebra persued by us over the last few years 2,3 has an intimate connection with this approach. In fact our formulation gives a more general framework allowing construction of a wide range of Lax operators of lattice models and recovers the corresponding result of ref 1 related to Uqsl(2) as a particular case. Another convincing demonstration of the usefulness of our approach is that, the well known Lax operator of the lattice Liouville model 4 as well as the recently discovered 5 nontrivial spectral parameter dependent variant of it can be constructed directly and easily from our general form,
A new type of Yang-Baxter equation (YBE) for RRR-operators depending on three spectral parameters is constructed from the star-triangle relation for the chiral Potts model. As the ZNZ_NZN​ symmetric generalization to the Ising model, its Boltzmann weights are known to depend on two variables describing a curve with genus larger than one for N>2N>2N>2, except for the self-dual point corresponding to the Fateev-Zamolodchikov chain. Combined with the fact that quantum Hamiltonians of edge-type models such as the Ising model contain both nearest-neighbor interaction and onsite potential terms, this leads naturally to an additional spectral parameter in the associated RRR-operator. The construction extends the edge-vertex correspondence of solvable lattice models, and provides a bridge between the Bazhanov-Stroganov four-parameter RRR-matrix---realized as an intertwiner of cyclic representations of Uq(sl2)U_q(\mathfrak{sl}_2)Uq​(sl2​) at a root of unity---and Shastry's two-parameter RRR-operator obtained from the decorated YBE.
Starting from the Kauffman-Lomonaco braiding matrix transforming the natural basis to Bell states, the spectral parameter describing the entanglement is introduced through Yang-Baxterization. It gives rise to a new type of solutions for Yang-Baxter equation, called the type-II that differs from the familiar solution called type-I of YBE associated with the usual chain models. The Majorana fermionic version of type-II yields the Kitaev Hamiltonian. The introduced ℓ 1 -norm leads to the maximum of the entanglement by taking the extreme value and shows that it is related to the Wigner's D-function. Based on the Yang-Baxter equation the 3-body S-Matrix for type-II is explicitly given. Different from the type-I solution, the type-II solution of YBE should be considered in describing quantum information. The idea is further extended to 3 parafermion model based on SU (3) principal representation. The type-II is in difference from the familiar type-I in many respects. For example, the quantities corresponding to velocity in the chain models obey the Lorentzian additivity rather than Galilean rule ( u + v ). Most possibly, for the type-II solutions of YBE there may not exist RTT relation. Further more, for 3 parafermion model we only need the rational Yang-Baxterization, which seems like trigonometric. Similar discussions are also made in terms of generalized Yang-Baxter equation with three spin spaces .
The Yang-Baxter Equation (YBE) plays a crucial role for studying integrable many-body quantum systems. Many known YBE solutions provide various examples ranging from quantum spin chains to superconducting systems. Models of solvable statistical mechanics and their avatars are also based on YBE. Therefore, new solutions of the YBE could be used to construct new interesting 1D quantum or 2D classical systems with many other far-reaching applications. In this work, we attempt to find (almost) exhaustive set of solutions for the YBE in the lowest dimensions corresponding to a two-qubit case. We develop an algorithm, which can potentially be used for generating new higher-dimensional solutions of the YBE.