Integrable models of coupled Heisenberg chains

Natan Andrei, Henrik Johannesson

Kuppuswamy Porsezian

Holger Frahm, Claus Rödenbeck

We show that the solutions of the Yang-Baxter equation invariant under the action of the Yangian Y ( sl 2 ) lead to inhomogeneous vertex models. Starting from a four-dimensional representation of Y ( sl 2 ), we obtain an integrable family of coupled Heisenberg spin-½ chains. Some thermodynamical properties of this model are studied by means of the algebraic Bethe ansatz.

Robin Steinigeweg, Heinz–Jürgen Schmidt

Kong-Ju-Bock Lee, P. Schlottmann

We construct an integrable SU(2)-invariant model consisting of the Heisenberg chain of spin 1 interacting with an impurity of spin S. This generalizes previous results by Andrei and Johannesson for the spin-(1/2 chain. The model Hamiltonian is diagonalized and the thermodynamics is obtained. For ferromagnetic coupling at low temperatures the impurity susceptibility diverges as ${T}^{\mathrm{\ensuremath{-}}2}$ and the impurity specific heat is proportional to ${T}^{1/2}$ for all values of the impurity spin S. For antiferromagnetic coupling and T=0 the impurity susceptibility diverges proportionally to \ensuremath{\Vert}lnH\ensuremath{\Vert} as H\ensuremath{\rightarrow}0 if S=(1/2, while if S>1 the impurity spin is only partially compensated for by the S=1 chain.

Peter Jung, R. W. Helmes, Achim Rosch

The heat conductivity $\ensuremath{\kappa}(T)$ of integrable models, like the one-dimensional spin-$1/2$ nearest-neighbor Heisenberg model, is infinite even at finite temperatures as a consequence of the conservation laws associated with integrability. Small perturbations lead to finite but large transport coefficients which we calculate perturbatively using exact diagonalization and moment expansions. We show that there are two different classes of perturbations. While an interchain coupling of strength ${J}_{\ensuremath{\perp}}$ leads to $\ensuremath{\kappa}(T)\ensuremath{\propto}1/{J}_{\ensuremath{\perp}}^{2}$ as expected from simple golden-rule arguments, we obtain a much larger $\ensuremath{\kappa}(T)\ensuremath{\propto}1/{J}^{\ensuremath{'}4}$ for a weak next-nearest-neighbor interaction ${J}^{\ensuremath{'}}$. This can be explained by a new approximate conservation law of the $J\mathrm{\text{\ensuremath{-}}}{J}^{\ensuremath{'}}$ Heisenberg chain.