On the ground state energy scaling in quasi-rung-dimerized spin ladders

On the basis of periodic boundary conditions we study perturbatively a large N asymptotics (N is the number of rungs) for the ground state energy density and gas parameter of a spin ladder with slightly destroyed rung-dimerization. Exactly rung-dimerized spin ladder is treated as the reference model. Explicit perturbative formulas are obtained for three special classes of spin ladders.Comment: 4 page

Perturbation theories for the S=1/2 spin ladder with four-spin ring exchange

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 $\eta\simeq1$, in agreement both with exact results available for the dimer line and with the bosonization analysis. The phase emerging for high values of the ring exchange is argued to be gapped and spontaneously dimerized. The results for the transition line from strong coupling and from weak coupling match with each other naturally.Comment: 8 pages, 4 figures, some minor changes in text and reference

Rung-singlet phase of the S=1/2 two-leg spin-ladder with four-spin cyclic exchange

Using continuous unitary transformations (CUT) we calculate the one-triplet gap for the antiferromagnetic S=1/2 two-leg spin ladder with additional four-spin exchange interactions in a high order series expansion about the limit of isolated rungs. By applying a novel extrapolation technique we calculate the transition line between the rung-singlet phase and a spontaneously dimerized phase with dimers on the legs. Using this efficient extrapolation technique we are able to analyze the crossover from strong rung coupling to weakly coupled chains.Comment: 4 pages, 4 figures included, submitted to Phys Rev

Phase Diagram of a Spin Ladder with Cyclic Four Spin Exchange

We present the phase diagram of the $S=1/2$ Heisenberg model on the two leg ladder with cyclic four spin exchange, determined by a combination of Exact Diagonalization and Density Matrix Renormalization Group techniques. We find six different phases and regimes: the rung singlet phase, a ferromagnetic phase, two symmetry broken phases with staggered dimers and staggered scalar chiralities, and a gapped region with dominant vector chirality or collinear spin correlations. We localize the phase transitions and investigate their nature.Comment: 4 pages, 6 figures, REVTeX 4, published versio

Phase diagrams of the generalized spin-1/2 ladder under staggered field and dimerization: A renormalization group study

In the weak-coupling regime of the continuous theories, two sets of one-loop renormalization group equations are derived and solved to disclose the phase diagrams of the antiferromagnetic generalized two-leg spin-1/2 ladder under the effect of (I) a staggered external magnetic field and (II) an explicit dimerization. In model (I), the splitting of the SU(2)$_2$ critical line into U(1) and Z$_2$ critical surfaces is observed; while in model (II), two critical surfaces arising from their underlying critical lines with SU(2)$_2$ and Z$_2$ characteristics merge into an SU(2)$_1$ critical surface on the line where the model attains its highest symmetry.Comment: 10 pages, 9 figure

Staggered dimer order in S=1/2 quantum spin ladder system with four spin exchange

We study the S=1/2 quantum spin ladder system with the four-spin exchange, using density matrix renormalization group method and an exact diagonalization method. Recently, the phase transition in this system and its universality class are studied. But there remain controversies whether the phase transition is second order type or the other type and the nature of order parameter. There are arguments that the massless phase appears. But this does not agree with our previous result. Analyzing DMRG data, we try a new approach in order to determine a phase which appears after the phase transition. We find that the edge state appears in the open boundary condition, investigating excitation energies of states with higher magnetizations.Comment: Submitted to Phys. Rev. B, (REVTeX4

Phase Diagram of the Heisenberg Spin Ladder with Ring Exchange

We investigate the phase diagram of a generalized spin-1/2 quantum antiferromagnet on a ladder with rung, leg, diagonal, and ring-exchange interactions. We consider the exactly soluble models associated with the problem, obtain the exact ground states which exist for certain parameter regimes, and apply a variety of perturbative techniques in the regime of strong ring-exchange coupling. By combining these approaches with considerations related to the discrete Z_4 symmetry of the model, we present the complete phase diagram.Comment: 17 pages, 10 figure

Magnetic Phase Diagram of Spin-1/2 Two-Leg Ladder with Four-Spin Ring Exchange

We study the spin-1/2 two-leg Heisenberg ladder with four-spin ring exchanges under a magnetic field. We introduce an exact duality transformation which is an extension of the spin-chirality duality developed previously and yields a new self-dual surface in the parameter space. We then determine the magnetic phase diagram using the numerical approaches of the density-matrix renormalization-group and exact diagonalization methods. We demonstrate the appearance of a magnetization plateau and the Tomonaga-Luttinger liquid with dominant vector-chirality quasi-long-range order for a wide parameter regime of strong ring exchange. A "nematic" phase, in which magnons form bound pairs and the magnon-pairing correlation functions dominate, is also identified.Comment: 18pages, 7 figure

Optical absorption spectra in SrCu_2O_3 two-leg spin ladder

We calculate the phonon-assisted optical-absorption spectra in SrCu_2O_3 two-leg spin-ladder systems. The results for two models proposed for SrCu_2O_3 are compared. In the model including the effects of a cyclic four-spin interaction, the shoulder structure appears at 978 cm^{-1} and the peak appears at 1975 cm^{-1} in the spectrum for polarization of the electric field parallel to the legs. In the other model which describes a pure two-leg ladder, the peak appears around the lower edge of the spectrum at 1344 cm^{-1}. The feature can be effective in determining the proper model for SrCu_2O_3.Comment: 5 pages, 5 figures, to appear in PRB vol. 67 (2003