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On the Form Factors of Local Operators in the Bazhanov–Stroganov and Chiral Potts Models

Nicolas Grosjean, Jean Michel Maillet, Giuliano Niccoli

arXiv:1309.4701Annales Henri PoincaréOct 22, 201445 citations

Eigenvectors of Baxter–Bazhanov–Stroganov τ (2) (tq) model with fixed-spin boundary conditions

N. Z. Iorgov, V. N. Shadura, Yu Tykhyy

We give explicit formulas for the eigenvectors of the transfer matrix of the Baxter-Bazhanov-Stroganov (BBS) model (N-state spin model) with fixed-spin boundary conditions. We obtain these formulas from the formulas for the eigenvectors of the periodic BBS model by a limit procedure. The latter formulas were derived in the framework of Sklyanin’s method of separation of variables. In the case of fixed-spin boundaries, we solve the corresponding T-Q Baxter equations for the functions of separated variables explicitly. As a particular case, we obtain the eigenvectors of the Hamiltonian of the Ising-like ℤN quantum chain model.We give explicit formulas for the eigenvectors of the transfer matrix of the Baxter-Bazhanov-Stroganov (BBS) model (N-state spin model) with fixed-spin boundary conditions. We obtain these formulas from the formulas for the eigenvectors of the periodic BBS model by a limit procedure. The latter formulas were derived in the framework of Sklyanin’s method of separation of variables. In the case of fixed-spin boundaries, we solve the corresponding T-Q Baxter equations for the functions of separated variables explicitly. As a particular case, we obtain the eigenvectors of the Hamiltonian of the Ising-like ℤN quantum chain model.

Nov 21, 20122 citations

Baxter operators for arbitrary spin II

Dmitry Chicherin, Sergey E. Derkachov, David Roudolph Karakhanyan +1 more

arXiv:1107.0643Nuclear Physics BSep 3, 201118 citations

Baxter operators for arbitrary spin

Dmitry Chicherin, Sergey E. Derkachov, David Roudolph Karakhanyan +1 more

arXiv:1106.4991Nuclear Physics BSep 10, 201116 citations

Transfer matrix eigenvectors of the Baxter–Bazhanov–Stroganov τ2-model forN= 2

O. Lisovyy

We find a representation of the row-to-row transfer matrix of the Baxter–Bazhanov–Stroganov τ 2 -model for N = 2 in terms of an integral over two commuting sets of Grassmann variables. Using this representation, we explicitly calculate transfer matrix eigenvectors and normalize them. It is also shown how form factors of the model can be expressed in terms of determinants and inverses of certain Toeplitz matrices.

arXiv:nlin/0512026Journal of Physics A Mathematical and GeneralFeb 22, 200613 citations

The Baxter–Bazhanov–Stroganov model: separation of variables and the Baxter equation

G von Gehlen, N. Z. Iorgov, S Pakuliak +1 more

The Baxter-Bazhanov-Stroganov model (also known as the τ^(2) model) has attracted much interest because it provides a tool for solving the integrable chiral Z_N-Potts model. It can be formulated as a face spin model or via cyclic L-operators. Using the latter formulation and the Sklyanin-Kharchev-Lebedev approach, we give the explicit derivation of the eigenvectors of the component B_n(λ) of the monodromy matrix for the fully inhomogeneous chain of finite length. For the periodic chain we obtain the Baxter T-Q-equations via separation of variables. The functional relations for the transfer matrices of the τ^(2) model guarantee non-trivial solutions to the Baxter equations. For the N=2 case, which is free fermion point of a generalized Ising model, the Baxter equations are solved explicitly.The Baxter-Bazhanov-Stroganov model (also known as the τ^(2) model) has attracted much interest because it provides a tool for solving the integrable chiral Z_N-Potts model. It can be formulated as a face spin model or via cyclic L-operators. Using the latter formulation and the Sklyanin-Kharchev-Lebedev approach, we give the explicit derivation of the eigenvectors of the component B_n(λ) of the monodromy matrix for the fully inhomogeneous chain of finite length. For the periodic chain we obtain the Baxter T-Q-equations via separation of variables. The functional relations for the transfer matrices of the τ^(2) model guarantee non-trivial solutions to the Baxter equations. For the N=2 case, which is free fermion point of a generalized Ising model, the Baxter equations are solved explicitly.

arXiv:nlin/0603028Journal of Physics A Mathematical and GeneralMay 23, 200664 citations

Eigenvectors of the Baxter-Bazhanov-Stroganov τ(2)(t q ) model with fixed-spin boundary conditions

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