Multi-leg integrable ladder models

Costas John Efthimiou

Naomichi Hatano, Y Nishiyama

The S=1/2 antiferromagnetic Heisenberg model on multi-leg ladders is investigated. Criticality of the ground-state transition is explored by means of finite-size scaling. The ladders with an even number of legs and those with an odd number of legs are distinguished clearly. In the former, the energy gap opens up as Delta E approximately J perpendicular to , where J perpendicular to is the strength of the antiferromagnetic inter-chain coupling. In the latter, the critical phase with the central charge c=1 extends over the whole region of J perpendicular to >0.

N. M. Bogoliubov, Cyril Leonidovich Malyshev

D. Arnaudon, A. Sedrakyan, Tigran Sedrakyan

We construct integrable spin chains with the inhomogeneous periodic disposition of the anisotropy parameter. The periodicity holds for both auxiliary (space) and quantum (time) directions. The integrability of the model is based on a set of coupled Yang–Baxter equations. This construction yields the P-leg integrable ladder Hamiltonians. We analyse the corresponding quantum group symmetry.

Joel Feldman, Horst Knörrer, Eugene Trubowitz B

Jianhui Dai, P. Schlottmann, Yupeng Wang

We study boundary rung defects in n-leg quantum spin ladders with $\mathrm{SU}{(2}^{n})$ leg symmetry. The rung interactions are parametrized by two coupling parameters J and ${J}^{\ensuremath{'}}$ interpolating between the uniform spin tube ${(J}^{\ensuremath{'}}=J)$ and the open spin ladder ${(J}^{\ensuremath{'}}=0).$ The rung defect at the edge of the ladder has rung coupling parameters ${J}_{d}$ and ${J}_{d}^{\ensuremath{'}}.$ The conditions for the integrability of the model are investigated as a function of n, J, ${J}^{\ensuremath{'}},$ ${J}_{d},$ and ${J}_{d}^{\ensuremath{'}},$ and the Bethe Ansatz equations for the exact solution are derived. The boundary quantum critical behavior is discussed. The conditions for the formation of a local moment (boundary bound state due to the defect) are studied. In the absence of a magnetic field such a bound state is only possible for even-legged spin tubes, while for odd-legged ladders a bound state can only occur in a large magnetic field. Depending on the parameters of the host this local moment may be screened in analogy to the Kondo effect.