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arXiv:cond-mat/0206081 · Physical review. B, Condensed matter

Perturbation theories for the S=12 spin ladder with a four-spin ring exchange

M. Müller, T. Vekua, H.-J. Mikeska

Published Oct 29, 2002• 57 citations
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Abstract

The isotropic $S=1/2$ antiferromagnetic spin ladder with additional four-spin ring exchange is studied perturbatively in the strong coupling regime with the help of cluster expansion technique, and by means of bosonization in the weak coupling limit. It is found that a sufficiently large strength of ring exchange leads to a second-order phase transition, and the shape of the boundary in the vicinity of the known exact transition point is obtained. The critical exponent for the gap is found to be $\ensuremath{\eta}\ensuremath{\simeq}1,$ in agreement both with exact results available for the dimer line and with the bosonization analysis. The phase we determined after crossing the critical line is gapped and spontaneously dimerized. The results for the transition line from strong coupling and from weak coupling match with each other naturally.

DOI
10.1103/physrevb.66.134423

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The isotropic S=1/2S=1/2S=1/2 antiferromagnetic spin ladder with additional four-spin ring exchange is studied perturbatively in the strong coupling regime with the help of cluster expansion technique, and by means of bosonization in the weak coupling limit. It is found that a sufficiently large strength of ring exchange leads to a second-order phase transition, and the shape of the boundary in the vicinity of the known exact transition point is obtained. The critical exponent for the gap is found to be \ensuremathη\ensuremath≃1,\ensuremath{\eta}\ensuremath{\simeq}1,\ensuremathη\ensuremath≃1, in agreement both with exact results available for the dimer line and with the bosonization analysis. The phase we determined after crossing the critical line is gapped and spontaneously dimerized. The results for the transition line from strong coupling and from weak coupling match with each other naturally.
Using continuous unitary transformations (CUTs) we calculate the one-triplet gap for the antiferromagnetic S=12S=\frac{1}{2}S=21​ two-leg spin ladder with additional four-spin exchange interactions in a high order series expansion about the limit of isolated rungs. By applying an efficient extrapolation technique we calculate the transition line between the rung-singlet phase and a spontaneously dimerized phase with dimers on the legs. Using this extrapolation technique we are able to analyze the crossover from strong rung coupling to weakly coupled chains.
We study an S=12S=\frac{1}{2}S=21​ quantum-spin ladder system with four-spin cyclic exchange, using the density matrix renormalization group (DMRG) and exact diagonalization methods. Recently, the phase transition and its universality class in this system have been studied. However, controversies remain on whether the phase transition is second-order type or another type and on the nature of critical phenomena. In addition, there are several arguments concerning where the transition point is. Analyzing DMRG data, we use an approach to determine the ordered phase which appears after the phase transition. We find that the edge state appears under the open boundary condition by investigating excitation energies of states with higher magnetizations. We also estimate the correlation length and discuss the critical behavior.
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We study a phase transition and critical properties of the quantum spin ladder system with a four-spin interaction. We determine a phase boundary between a rung singlet and a staggered dimer phases numerically. This phase transition is of a second order in the weak-coupling region. We confirm that this universality class is described by the k=2k=2k=2 SU(2) Wess-Zumino-Witten model, analyzing the central charge and scaling dimensions. In the strong-coupling region, phase transition becomes of a first order.
We study the ground-state phase diagram of a spin-12\frac{1}{2}21​ frustrated XXZ ladder, in which two antiferromagnetic chains are coupled by competing rung and diagonal interactions, ${J}_{\ensuremath{\perp}}$ and ${J}_{\ifmmode\times\else\texttimes\fi{}}$. Previous studies on the isotropic model have revealed that a fluctuation-induced effective dimer attraction between the legs stabilizes the columnar dimer (CD) phase in the highly frustrated regime ${J}_{\ensuremath{\perp}}\ensuremath{\approx}2{J}_{\ifmmode\times\else\texttimes\fi{}}$, especially for ferromagnetic ${J}_{\ensuremath{\perp},\ifmmode\times\else\texttimes\fi{}}<0$. By means of effective field theory and numerical analyses, we extend this analysis to the XXZ model, and we obtain a rich phase diagram. The diagram includes four gapped featureless phases with no symmetry breaking: the rung singlet (RS) and Haldane phases as well as their twisted variants, the RS* and Haldane* phases, which are all distinct in the presence of certain symmetries. Significantly, the Haldane-CD transition point in the isotropic model turns out to be a crossing point of two transition lines in the XXZ model, and the stripe N\'eel and RS* phases appear between these lines. This indicates a nontrivial interplay between the effective dimer attraction and the exchange anisotropy. In the easy-plane regime, the four featureless phases and two critical phases are found to compete in a complex manner depending on the signs of ${J}_{\ensuremath{\perp},\ifmmode\times\else\texttimes\fi{}}$.
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