Integrability of spin chain with boundary impurities

Bo-Yu Hou, Kangjie Shi, Rui‐Hong Yue +1 more

Bo-Yu Hou, Kangjie Shi, Rui‐Hong Yue +1 more

We show the integrability of spin-½ XXZ Heisenberg chain with two arbitrary spin boundary impurities. By using the fusion method, we generalize it to the spin-1 XXZ chain. Then the eigenvalues of Hamiltonians of these models are obtained by the means of Bethe ansatz method.

Stefan Rommer, Sebastian Eggert

Jianhui Dai, Yupeng Wang, Ulrich Eckern

We study the impurity-induced critical behavior in an integrable $\mathrm{SU}(2)$-invariant model consisting of an open spin chain of arbitrary spin $S$ (Takhatajian-Babujian model) interacting with an impurity of spin ${S}^{\ensuremath{'}}$ located at one of the boundaries. For $S=1/2$ or ${S}^{\ensuremath{'}}=1/2,$ the impurity interaction takes a very simple form $J{S}_{1}\ensuremath{\cdot}{S}^{\ensuremath{'}}$ that describes the deformed boundary bond between the impurity ${S}^{\ensuremath{'}}$ and the first bulk spin ${S}_{1}$ with an arbitrary coupling strength $J.$ For a weak coupling $0<J<{J}_{0}/[{(S+S}^{\ensuremath{'}}{)}^{2}\ensuremath{-}1/4],$ the impurity is completely compensated, undercompensated, and overcompensated for ${S}^{\ensuremath{'}}=S,$ ${S}^{\ensuremath{'}}>S,$ and ${S}^{\ensuremath{'}}<S$ as in the usual Kondo problem. While for strong coupling $J>~{J}_{0}/[{(S+S}^{\ensuremath{'}}{)}^{2}\ensuremath{-}1/4],$ the impurity spin is split into two ghost spins. Their cooperative effect leads to a variety of new critical behaviors with different values of $|{S}^{\ensuremath{'}}\ensuremath{-}S|.$

V. I. Inozemtsev

Bo-Yu Hou, Shi Kang-Jie, Rui‐Hong Yue +1 more

By using the fusion method, we give the spin-1 XXX chain associated with sl 2 with two arbitrary spin boundary impurities. Then the exact diagonalized Hamiltonian of this model was obtained by the means of Bethe ansatz method.