scholarly journals The transfer matrix of a superintegrable chiral Potts model as theQoperator of root-of-unity XXZ chain with cyclic representation of U_{\mathsf {q}}(sl_2)

2007 ◽  
Vol 2007 (09) ◽  
pp. P09021-P09021 ◽  
Author(s):  
Shi-shyr Roan
Keyword(s):  
Transfer Matrix ◽  
Potts Model ◽  
Chiral Potts Model ◽  
Root Of Unity ◽  
Cyclic Representation ◽  
Xxz Chain

scholarly journals QUASI-PARTICLES IN THE CHIRAL POTTS MODEL

1994 ◽  
Vol 08 (25n26) ◽  
pp. 3601-3621 ◽  
Author(s):  
RINAT KEDEM ◽  
BARRY M. McCOY
Keyword(s):  
Transfer Matrix ◽  
Potts Model ◽  
Numerical Study ◽  
Particle Spectrum ◽  
Exact Results ◽  
Chiral Potts Model ◽  
Quasi Particle ◽  
Massive Phase ◽  
Matrix Eigenvalues ◽  
Potts Chain

We study the quasi-particle spectrum of the integrable three-state chiral Potts chain in the massive phase by combining a numerical study of the zeros of associated transfer matrix eigenvalues with the exact results of the ferromagnetic three-state Potts chain and the three-state superintegrable chiral Potts model. We find that the spectrum is described in terms of quasi-particles with momenta restricted only to segments of the Brillouin zone 0≤P≤2π where the boundaries of the segments depend on the chiral angles of the model.

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: CORNER TRANSFER MATRICES AND PARAMETRIZATIONS

1993 ◽  
Vol 07 (20n21) ◽  
pp. 3489-3500 ◽  
Author(s):  
R.J. BAXTER
Keyword(s):  
Transfer Matrix ◽  
Potts Model ◽  
Transfer Matrix Method ◽  
Matrix Method ◽  
Weight Functions ◽  
Chiral Potts Model ◽  
Transfer Matrices ◽  
Corner Transfer Matrices ◽  
Difference Property ◽  
The Difference

We consider the star-triangle relation and the form of its solutions. We present some simple parametrizations of the weight functions of the three-state chiral Potts model. This model does not have the “difference property”: we discuss the resulting difficulties in attempting to use the corner transfer matrix method for this model.

scholarly journals On the Q operator and the spectrum of the XXZ model at root of unity

2021 ◽  
Vol 11 (3) ◽  
Author(s):  
Yuan Miao ◽  
Jules Lamers ◽  
Vincent Pasquier
Keyword(s):  
Transfer Matrix ◽  
Integrable Model ◽  
Xxz Model ◽  
Root Of Unity ◽  
Finite Dimensional ◽  
Xxz Chain ◽  
Potential Applications ◽  
Complex Spin ◽  
Matrix Fusion ◽  
Arbitrary Anisotropy

The spin-\frac{1}{2}12 Heisenberg XXZ chain is a paradigmatic quantum integrable model. Although it can be solved exactly via Bethe ansatz techniques, there are still open issues regarding the spectrum at root of unity values of the anisotropy. We construct Baxter’s Q operator at arbitrary anisotropy from a two-parameter transfer matrix associated to a complex-spin auxiliary space. A decomposition of this transfer matrix provides a simple proof of the transfer matrix fusion and Wronskian relations. At root of unity a truncation allows us to construct the Q operator explicitly in terms of finite-dimensional matrices. From its decomposition we derive truncated fusion and Wronskian relations as well as an interpolation-type formula that has been conjectured previously. We elucidate the Fabricius–McCoy (FM) strings and exponential degeneracies in the spectrum of the six-vertex transfer matrix at root of unity. Using a semicyclic auxiliary representation we give a conjecture for creation and annihilation operators of FM strings for all roots of unity. We connect our findings with the `string-charge duality’ in the thermodynamic limit, leading to a conjecture for the imaginary part of the FM string centres with potential applications to out-of-equilibrium physics.

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