Heisenberg XYZ Hamiltonian with integrable impurities

Anastasia Doikou

Natan Andrei, Henrik Johannesson

Marcio Jose Martins

Lai Yun-zhong, Zhan-Ning Hu, Jun Liang +1 more

In this paper, we construct a Hamiltonian of the impurity model with next-nearest-neighbor interaction within the framework of the open boundary Heisenberg XYZ spin chain. This impurity model is an exactly solved one and it degenerates to the integrable XXZ impurity model under the triangular limit. It is the first approach to add the impurities and next-nearest-neighbor interaction to the integrable completely anisotropic Heisenberg spin chain. We find also that the impurity parameters in the bulk are real when the cross parameter is imaginary for the Hermitian Hamiltonian, or vice versa, when the next-nearest-neighbor interaction is introduced. The eigenvalue of the Hamiltonian and the Bethe ansatz equations for the trigonometric limit case are derived also.

Paul Fendley, Sascha Gehrmann, Eric Vernier +1 more

Abstract Sutherland showed that the XYZ quantum spin-chain Hamiltonian commutes with the eight-vertex model transfer matrix, so that Baxter’s subsequent tour de force proves the integrability of both. The proof requires parametrising the Boltzmann weights using elliptic theta functions and showing they satisfy the Yang-Baxter equation. We here give a simpler derivation of the integrability of the XYZ chain by explicitly constructing an extensive sequence of conserved charges from a matrix-product operator. We show that they commute with the XYZ Hamiltonian with periodic boundary conditions or an arbitrary boundary magnetic field. A straightforward generalisation yields impurity interactions that preserve the integrability. Placing such an impurity at the edge gives an integrable generalisation of the Kondo problem with a gapped bulk. We make contact with the traditional approach by relating our matrix-product operator to products of the eight-vertex model transfer matrix.

Francisco Castilho Alcaraz, Walter Felipe Wreszinski