scholarly journals Bethe Ansatz and Symmetry in Superintegrable Chiral Potts Model and Root-of-unity Six-vertex Model

2006 ◽  
Author(s):  
Shi-shyr Roan
Keyword(s):  
Bethe Ansatz ◽  
Potts Model ◽  
Vertex Model ◽  
Chiral Potts Model ◽  
Root Of Unity

scholarly journals The Many Faces of the Chiral Potts Model

1997 ◽  
Vol 11 (01n02) ◽  
pp. 11-26 ◽  
Author(s):  
Helen Au-Yang ◽  
Jacques H.H. Perk
Keyword(s):  
Quantum Groups ◽  
Potts Model ◽  
Hypergeometric Functions ◽  
Chiral Potts Model ◽  
Root Of Unity ◽  
Basic Hypergeometric Functions ◽  
Higher Genus ◽  
The Many

In this talk, we give a brief overview of several aspects of the theory of the chiral Potts model, including higher-genus solutions of the star–triangle and tetrahedron equations, cyclic representations of affine quantum groups, basic hypergeometric functions at root of unity, and possible applications.

Chiral Potts model as a descendant of the six-vertex model

1990 ◽  
Vol 59 (3-4) ◽  
pp. 799-817 ◽  
Author(s):  
V. V. Bazhanov ◽  
Yu. G. Stroganov
Keyword(s):  
Potts Model ◽  
Vertex Model ◽  
Chiral Potts Model

FUNCTIONAL RELATIONS FOR TRANSFER MATRICES OF THE CHIRAL POTTS MODEL

1990 ◽  
Vol 04 (05) ◽  
pp. 803-870 ◽  
Author(s):  
R.J. Baxter ◽  
V.V. Bazhanov ◽  
J.H.H. Perk
Keyword(s):  
Potts Model ◽  
Finite Size ◽  
State Model ◽  
Integrable Case ◽  
Vertex Model ◽  
Chiral Potts Model ◽  
Transfer Matrices ◽  
Functional Relations ◽  
Finite Size Corrections

It has recently been shown that the solvable N-state chiral Potts model is related to a vertex model with N-state spins on vertical edges, two-state spins on horizontal edges. Here we generalize this to a “j-state by N-state” model and establish three sets of functional relations between the various transfer matrices. The significance of the “super-integrable” case of the chiral Potts model is discussed, and results reported for its finite-size corrections at criticality.

CYCLIC MONODROMY MATRICES FOR THE R-MATRIX OF THE SIX-VERTEX MODEL AND THE CHIRAL POTTS MODEL WITH FIXED SPIN BOUNDARY CONDITIONS

1992 ◽  
Vol 07 (supp01b) ◽  
pp. 963-975 ◽  
Author(s):  
VITALY O. TARASOV
Keyword(s):  
Boundary Conditions ◽  
Potts Model ◽  
Vertex Model ◽  
Chiral Potts Model ◽  
Transfer Matrices ◽  
Direct Computation ◽  
R Matrix ◽  
Monodromy Matrices

Irreducible cyclic representations of the algebra of monodromy matrices corresponding to the R-matrix of the six-vertex model are described. As a consequence, the direct computation of spectra for transfer-matrices of the chiral Potts model with special fixed-spin boundary conditions is done. The generalization of simple Baxter's Hamiltonian is proposed.

scholarly journals Quantum relativistic Toda chain at root of unity: isospectrality, modifiedQ-operator, and functional Bethe ansatz

2002 ◽  
Vol 31 (9) ◽  
pp. 513-553 ◽  
Author(s):  
Stanislav Pakuliak ◽  
Sergei Sergeev
Keyword(s):  
Bethe Ansatz ◽  
Weyl Algebra ◽  
Separation Of Variables ◽  
Toda Chain ◽  
Special Choice ◽  
Finite Dimensional Representation ◽  
Classical Counterpart ◽  
Discrete Integrable System ◽  
Root Of Unity ◽  
Finite Dimensional

We investigate anN-state spin model called quantum relativistic Toda chain and based on the unitary finite-dimensional representations of the Weyl algebra withqbeingNth primitive root of unity. Parameters of the finite-dimensional representation of the local Weyl algebra form the classical discrete integrable system. Nontrivial dynamics of the classical counterpart corresponds to isospectral transformations of the spin system. Similarity operators are constructed with the help of modified Baxter'sQ-operators. The classical counterpart of the modifiedQ-operator for the initial homogeneous spin chain is a Bäcklund transformation. This transformation creates an extra Hirota-type soliton in a parameterization of the chain structure. Special choice of values of solitonic amplitudes yields a degeneration of spin eigenstates, leading to the quantum separation of variables, or the functional Bethe ansatz. A projector to the separated eigenstates is constructed explicitly as a product of modifiedQ-operators.

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