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arXiv:cond-mat/0009073 · Physical review. B, Condensed matter

Open su(4)-invariant spin ladder with boundary defects

Yupeng Wang, P. Schlottmann

Published Aug 1, 2000• 14 citations
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Abstract

The integrable su(4)-invariant spin-ladder model with a boundary defect is studied using the Bethe ansatz method. The exact phase diagram for the ground state is given and the boundary quantum critical behavior is discussed. It consists of a gapped phase in which the rungs of the ladder form singlet states and a gapless Luttinger liquid phase. It is found that in the gapped phase the boundary bound state corresponds to an unscreened local moment, while in the Luttinger liquid phase the local moment is screened at low temperatures in analogy to the Kondo effect.

DOI
10.1103/physrevb.62.3845

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The integrable su(4)-invariant spin-ladder model with a boundary defect is studied using the Bethe ansatz method. The exact phase diagram for the ground state is given and the boundary quantum critical behavior is discussed. It consists of a gapped phase in which the rungs of the ladder form singlet states and a gapless Luttinger liquid phase. It is found that in the gapped phase the boundary bound state corresponds to an unscreened local moment, while in the Luttinger liquid phase the local moment is screened at low temperatures in analogy to the Kondo effect.
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We study boundary rung defects in n-leg quantum spin ladders with SU(2n)\mathrm{SU}{(2}^{n})SU(2n) 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 Jd{J}_{d}Jd​ and ${J}_{d}^{\ensuremath{'}}.$ The conditions for the integrability of the model are investigated as a function of n, J, ${J}^{\ensuremath{'}},$ Jd,{J}_{d},Jd​, 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.
We investigate the low-temperature phase diagram of the exactly solved su (4) two-leg spin ladder as a function of the rung coupling and magnetic field H by means of the thermodynamic Bethe ansatz (TBA). In the absence of a magnetic field the model exhibits three quantum phases, while in the presence of a strong magnetic field there is no singlet ground state for ferromagnetic rung coupling. For antiferromagnetic rung coupling, there is a gapped phase in the regime H < H c1 , a fully polarized gapped phase for H > H c2 and a Luttinger liquid magnetic phase in the regime H c1 < H < H c2 . The critical behaviour derived using the TBA is consistent with the existing experimental, numerical and perturbative results for the strong coupling ladder compounds. This includes the spin excitation gap and the critical fields H c1 and H c2 , which are in excellent agreement with the experimental values for the known strong coupling ladder compounds (5IAP) 2 CuBr 4 ·2H 2 O, Cu 2 (C 5 H 12 N 2 ) 2 Cl 4 and (C 5 H 12 N) 2 CuBr 4 . In addition we predict the spin gap for the weak coupling compounds with , such as (VO) 2 P 2 O 7 , and also show that the gap opens for arbitrary .
A detailed study of an S = ½ spin ladder model is given. The ladder consists of plaquettes formed by nearest-neighbor rungs with all possible SU (2)-invariant interactions. For properly chosen coupling constants, the model is shown to be integrable in the sense that the quantum Yang-Baxter equation holds and one has an infinite number of conserved quantities. The R -matrix and L -operator associated with the model Hamiltonian are given in a limiting case. It is shown that after a simple transformation, the model can be solved via a Bethe ansatz. The phase diagram of the ground state is exactly derived using the Bethe ansatz equation.
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We present an integrable spin ladder model which possesses a free parameter besides the rung and leg couplings.The model is exactly solvable by means of the Bethe ansatz method.We determine the dependence on the anisotropy parameter of the phase transition between gapped and gapless spin excitations and present the phase diagram.Finally, we show that the model is a special case of a more general Hamiltonian with six free parameters.We also investigate the thermodynamics of the model.Specifically, the magnetic susceptibility as a function of the temperature is obtained numerically.The influence of this anisotropy parameter on these physical curves is determined explicitly.A comparsion between the spin gap obtained from the susceptibility curve and that one obtained from the Bethe ansatz equations is performed and a good agreement is found.