We review recent progress towards the solution of exactly solved isotropic vertex models with arbitrary toroidal boundary conditions.Quantum space transformations make it possible the diagonalization of the corresponding transfer matrices by means of the quantum inverse scattering method.Explicit expressions for the eigenvalues and Bethe ansatz equations of the twisted isotropic spin chains based on the $B_{n},$ $D_{n}$ and $C_{n}$ Lie algebras are presented.The applicability of this approach to the eight vertex model with non-diagonal twists is also discussed.We review recent progress towards the solution of exactly solved isotropic vertex models with arbitrary toroidal boundary conditions.Quantum space transformations make it possible the diagonalization of the corresponding transfer matrices by means of the quantum inverse scattering method.Explicit expressions for the eigenvalues and Bethe ansatz equations of the twisted isotropic spin chains based on the $B_{n},$ $D_{n}$ and $C_{n}$ Lie algebras are presented.The applicability of this approach to the eight vertex model with non-diagonal twists is also discussed.

数理解析研究所講究録Apr 1, 20060 citations

Solving the fusion hierarchies of D and E lattice models

Yu‐Kui Zhou, Weiwei Sun

Nuclear Physics BNov 1, 19970 citations

Discrete Hirota's Equation in Quantum Integrable Models

A. Zabrodin

The recent progress in revealing classical integrable structures in quantum models solved by Bethe ansatz is reviewed. Fusion relations for eigenvalues of quantum transfer matrices can be written in the form of classical Hirota's bilinear difference equation. This equation is also known as the completely discretized version of the 2D Toda lattice. We explain how one obtains the specific quantum results by solving the classical equation. The auxiliary linear problem for the Hirota equation is shown to generalize Baxter's T-Q relation.The recent progress in revealing classical integrable structures in quantum models solved by Bethe ansatz is reviewed. Fusion relations for eigenvalues of quantum transfer matrices can be written in the form of classical Hirota's bilinear difference equation. This equation is also known as the completely discretized version of the 2D Toda lattice. We explain how one obtains the specific quantum results by solving the classical equation. The auxiliary linear problem for the Hirota equation is shown to generalize Baxter's T-Q relation.

arXiv:hep-th/9610039International Journal of Modern Physics BOct 30, 199736 citations

Exact solution of the lattice models

Hector J. de Vega, Esther Lopes

Nuclear Physics BSep 1, 199123 citations

Discrete Hirota’s equation in quantum integrable models

Anton Vladimirovich Zabrodin

The recent progress in revealing classical integrable structures in quantum models solved by Bethe ansatz is reviewed. Fusion relations for eigenvalues of quantum transfer matrices can be written in the form of classical Hirota’s bilinear difference equation. This equation is also known as the completely discretized version of the 2D Toda lattice. We explain how one obtains the specific quantum results by solving the classical equation. The auxiliary linear problem for the Hirota equation is shown to generalize Baxter’s T-Q relation.The recent progress in revealing classical integrable structures in quantum models solved by Bethe ansatz is reviewed. Fusion relations for eigenvalues of quantum transfer matrices can be written in the form of classical Hirota’s bilinear difference equation. This equation is also known as the completely discretized version of the 2D Toda lattice. We explain how one obtains the specific quantum results by solving the classical equation. The auxiliary linear problem for the Hirota equation is shown to generalize Baxter’s T-Q relation.

Jan 1, 199655 citations

Studies of the lattice Anderson model

Yung‐Chang Cheng, J.W. Chen, Hsueh‐Ju Lin

Journal of Magnetism and Magnetic MaterialsFeb 1, 19950 citations

B_{n},

D_{n}

and

C_{n}

Lie algebras are presented.The applicability of this approach to the eight vertex model with non-diagonal twists is also discussed.