GENERALIZED SKLYANIN ALGEBRA AND INTEGRABLE LATTICE MODELS

1994 ◽  
Vol 09 (13) ◽  
pp. 2245-2281 ◽  
Author(s):  
YAS-HIRO QUANO
Keyword(s):  
Inverse Problem ◽  
Lattice Model ◽  
Lattice Models ◽  
Baxter Equation ◽  
Initial Condition ◽  
Infinite Dimensional ◽  
Integrable Lattice ◽  
Crossing Symmetry ◽  
Sklyanin Algebra ◽  
Integrable Lattice Models

We study three properties of the ℤn⊗ℤn-symmetric lattice model; i.e. the initial condition, the unitarity and the crossing symmetry. The scalar factors appearing in the unitarity and the crossing symmetry are explicitly obtained. The [Formula: see text]-Sklyanin algebra is introduced in the natural framework of the inverse problem for this model. We build both finite- and infinite-dimensional representations of the [Formula: see text]-Sklyanin algebra, and construct an [Formula: see text] generalization of the broken ℤN model. Furthermore, the Yang-Baxter equation for this new model is proved.

CONSTRUCTION OF INTEGRABLE QUANTUM LATTICE MODELS THROUGH SKLYANIN-LIKE ALGEBRAS

1992 ◽  
Vol 07 (01) ◽  
pp. 61-69 ◽  
Author(s):  
A. KUNDU ◽  
B. BASU MALLICK
Keyword(s):  
Systematic Approach ◽  
Group Structure ◽  
Lattice Models ◽  
Toda Chain ◽  
Quantum Lattice ◽  
Integrable Quantum ◽  
Integrable Lattice ◽  
Special Mention ◽  
Sklyanin Algebra ◽  
Integrable Lattice Models

A systematic approach for generation of integrable quantum lattice models exploiting the underlying Uq(2) quantum group structure as well as its multiparameter generalization is presented. We find an extension of trigonometric Sklyanin algebra and also its deformation through "symmetry breaking transformation," which after consistent bosonization (or q-bosonization) construct a series of integrable lattice models. A novel quantum solvable derivative NLS, a relativistic Toda chain and a lattice model involving q-oscillators warrant special mention. As an added advantage, along with the integrable models the corresponding quantum R-matrices are also specified.

scholarly journals Integrable lattice models and holography

2021 ◽  
Vol 2021 (2) ◽  
Author(s):  
Meer Ashwinkumar
Keyword(s):  
Correlation Functions ◽  
Three Dimensional ◽  
Lattice Models ◽  
Simons Theory ◽  
Boundary Theory ◽  
Baxter Equation ◽  
Rational Solutions ◽  
Integrable Lattice ◽  
Local Operators ◽  
Integrable Lattice Models

Abstract We study four-dimensional Chern-Simons theory on D × ℂ (where D is a disk), which is understood to describe rational solutions of the Yang-Baxter equation from the work of Costello, Witten and Yamazaki. We find that the theory is dual to a boundary theory, that is a three-dimensional analogue of the two-dimensional chiral WZW model. This boundary theory gives rise to a current algebra that turns out to be an “analytically-continued” toroidal Lie algebra. In addition, we show how certain bulk correlation functions of two and three Wilson lines can be captured by boundary correlation functions of local operators in the three-dimensional WZW model. In particular, we reproduce the leading and subleading nontrivial contributions to the rational R-matrix purely from the boundary theory.

YANG-BAXTER ALGEBRAS, INTEGRABLE THEORIES AND QUANTUM GROUPS

1989 ◽  
Vol 04 (10) ◽  
pp. 2371-2463 ◽  
Author(s):  
H.J. De VEGA
Keyword(s):  
Quantum Groups ◽  
Scaling Limit ◽  
Finite Size ◽  
Lattice Models ◽  
Physical Models ◽  
Quantum Field Theories ◽  
Integrable Lattice ◽  
Ba Construction ◽  
Integrable Lattice Models ◽  
Conformal Models

The Yang-Baxter-Zamolodchikov-Faddeev (YBZF) algebras and their many applications are the subject of this reivew. I start by the solvable lattice statistical models constructed from YBZF algebras. All two-dimensional integrable vertex models follow in this way and are solvable via Bethe Ansatz (BA) and their generalizations. The six-vertex model solution and its q(2q−1) vertex generalization including its nested BA construction are exposed. YBZF algebras and their associated physical models are classified in terms of simple Lie algebras. It is shown how these lattice models yield both solvable massive quantum field theories (QFT) and conformal models in appropriated scaling (continuous) limits within the lattice light-cone approach. The method of finite-size calculations from the BA is described as well as its applications to derive the conformal properties of integrable lattice models. It is conjectured that all integrable QFT and conformal models follow in a scaling limit from these YBZF algebras. A discussion on braid and quantum groups concludes this review.

INTEGRABLE LATTICE MODELS, GRAPHS AND MODULAR INVARIANT CONFORMAL FIELD THEORIES

1992 ◽  
Vol 07 (03) ◽  
pp. 407-500 ◽  
Author(s):  
P. DI FRANCESCO
Keyword(s):  
Lattice Models ◽  
Field Theories ◽  
Conformal Field Theories ◽  
Compact Lie Groups ◽  
Modular Invariant ◽  
Conformally Invariant ◽  
Conformal Field ◽  
Integrable Lattice ◽  
Modular Invariants ◽  
Integrable Lattice Models

We review the construction of integrable height models attached to graphs, in connection with compact Lie groups. The continuum limit of these models yields conformally invariant field theories. A direct relation between graphs and (Kac–Moody or coset) modular invariants is proposed.

scholarly journals Approximate conservation laws in perturbed integrable lattice models

2015 ◽  
Vol 92 (19) ◽  
Author(s):  
Marcin Mierzejewski ◽  
Tomaž Prosen ◽  
Peter Prelovšek
Keyword(s):  
Conservation Laws ◽  
Lattice Models ◽  
Integrable Lattice ◽  
Integrable Lattice Models

scholarly journals Conjectures on hidden Onsager algebra symmetries in interacting quantum lattice models

2021 ◽  
Vol 11 (3) ◽  
Author(s):  
Yuan Miao
Keyword(s):  
Lattice Models ◽  
Transfer Matrices ◽  
Xxz Model ◽  
Fusion Procedure ◽  
Root Of Unity ◽  
Integrable Lattice ◽  
Onsager Algebra ◽  
Cyclic Transfer ◽  
Integrable Lattice Models ◽  
Matrix Fusion

We conjecture the existence of hidden Onsager algebra symmetries in two interacting quantum integrable lattice models, i.e. spin-1/2 XXZ model and spin-1 Zamolodchikov-Fateev model at arbitrary root of unity values of the anisotropy. The conjectures relate the Onsager generators to the conserved charges obtained from semi-cyclic transfer matrices. The conjectures are motivated by two examples which are spin-1/2 XX model and spin-1 U(1)-invariant clock model. A novel construction of the semi-cyclic transfer matrices of spin-1 Zamolodchikov-Fateev model at arbitrary root of unity values of the anisotropy is carried out via the transfer matrix fusion procedure.

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