Quantum Transfer Matrix Approach to One-Dimensional Solvable Models

Hiroshi Betsuyaku

Jeffrey Robert Schmidt

The two-dimensional dimer problem is studied using the tools of modern solvable models. The transfer matrix is constructed from local monodromy matrices, and is diagonalized by a modified Bethe Ansatz that does not begin with a Bethe ground state, but rather with a pair of states transformed one into the other by the transfer matrix. The resulting Bethe eigenvectors have a structure very different from those constructed in other models from a ground state, and have some properties in common with the free-fermion eigenvectors of the squared transfer matrix encountered in the literature. PACS Nos.: 05.50+q, 02.10.Ox, 02.30.Ik, 05.20.–y

H. B. Thacker

The generalization of Lorentz invariance to solvable two-dimensional lattice fermion models has been formulated in terms of Baxter’s corner transfer matrix. In these models, the lattice Hamiltonian and boost operator are given by fermionized nearest-neighbor Heisenberg spin chain operators. The transformation properties of the local lattice fermion operators under a boost provide a natural and precise way of generalizing the chiral structure of a continuum Dirac field to the lattice. The resulting formulation differs from both the Wilson and staggered (Kogut-Susskind) prescriptions. In particular, an axial Q5 rotation is sitewise local, while the vector charge rotation mixes nearest neighbors on even and odd sublattices. One of the most interesting developments in the theory of solvable two-dimensional lattice statistics models is Baxter’s invention of the “corner transfer matrix ” (CTM)[[1]]. In the same sense that an ordinary (row-to-row) transfer matrix can be viewed as an operator which translates by one row of sites on a lattice, the CTM may be defined as an operator which rotates around a central

Anı́bal Iucci, Miguel A. Cazalilla, Thierry Giamarchi

J. Abad, José G. Esteve

The physics of the one dimensional chains provides an excellent ground for a rigourous study of different properties of solvable models and their experimental verification in quantum magnetic systems. It is known that these models are useful analysing many body problems and recently, they have been applied to the study of 1D systems model of real atoms that have become to be the object of experiments. One of the most popular model is the spin 1/2 chain

Tohru Koma