We develop a method to analyze the strong coupling limit of the Bethe ansatz equations supposed to give the spectrum of anomalous dimensions of the planar N = 4 gauge theory. This method is particularly adapted for the three rank-one sectors, su(2), su(1|1) and sl(2). We use the elliptic parametrization of the Bethe ansatz variables, which degenerates to a hyperbolic one in the strong coupling ...

In this work we study the quantum Toda lattice, developing the asymptotic Bethe ansatz method first used by Sutherland. Despite its known limitations we find, on comparing with Gutzwiller’s exact method, that it works well in this particular problem and in fact becomes exact as \ grows large. We calculate ground state and excitation energies for finite-sized lattices, identify excitations as ph...

There are (at least) two main approaches to solvable lattice models and their associated quantum spin chains: the Bethe ansatz [6] and the corner transfer matrix method [5]. In his paper [6], Bethe solved the Heisenberg spin chain based on the string hypothesis which asserts that the eigenvalues of the Hamiltonian form certain strings in the complex plane as the size of the system tends to infi...

A non homogeneous spin chain in the representations {3} and {3 * } of A 2 is analyzed. We find that the naive nested Bethe ansatz is not applicable to this case. A method inspired in the nested Bethe ansatz, that can be applied to more general cases, is developed for that chain. The solution for the eigenvalues of the trace of the monodromy matrix is given as two coupled Bethe equations differe...

A strongly correlated electron system associated with the quantum superalgebra Uq[osp(2|2)] is studied in the framework of the quantum inverse scattering method. By solving the graded reflection equation, two classes of boundary-reflection Kmatrices leading to four kinds of possible boundary interaction terms are found. Performing the algebraic Bethe ansatz, we diagonalize the two-level transfe...

Abstract. A new integrable model which is a variant of the one-dimensional Hubbard model is proposed. The integrability of the model is verified by presenting the associated quantum R-matrix which satisfies the Yang-Baxter equation. We argue that the new model possesses the SO(4) algebra symmetry, which contains a representation of the η-pairing SU(2) algebra and a spin SU(2) algebra. Additiona...

Abstract. We analyze the linear conductance of a semiconductor quantum wire containing a region where a local Rashba spin-orbit interaction is present. We show that Fano lineshapes appear in the conductance due to the formation of quasi bound states which interfere with the direct transmission along the wire, a mechanism that we term the Fano-Rashba effect. We obtain the numerical solution of t...