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Physical review. B, Condensed matter

Phase diagram of the S=12 two-leg spin ladder with staggered bond alternation

Kiyomi Okamoto

Published Jun 24, 2003• 17 citations
Publisher

Abstract

The ground state of the $S=1/2$ two-leg ladder with the staggered bond alternations is investigated. We have determined the precise phase diagram on the $\ensuremath{\delta}\ensuremath{-}{J}^{\ensuremath{'}}$ plane $(\ensuremath{\delta}$ and ${J}^{\ensuremath{'}}$ are the magnitudes of the bond alternation and the rung interaction, respectively), employing the level spectroscopic analysis of the numerical diagonalization data obtained by the Lanczos algorithm with the twisted boundary condition. The phase boundary between the leg-dimer state and the rung-dimer state near $(\ensuremath{\delta}{,J}^{\ensuremath{'}})=(0,0)$ is of the form ${J}^{\ensuremath{'}}\ensuremath{\propto}{\ensuremath{\delta}}^{0.69},$ which is consistent with the prediction ${J}^{\ensuremath{'}}\ensuremath{\propto}{\ensuremath{\delta}}^{2/3}$ by Mart\'{\i}n-Delgado, Duleksky, and Sierra, and also by Wang and Nersesyan, but not with ${J}^{\ensuremath{'}}\ensuremath{\propto}{\ensuremath{\delta}}^{2}$ by Cabra and Grynberg.

DOI
10.1103/physrevb.67.212408

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Phase Diagram of the Spin-12\frac{1}{2}21​ Bond-Alternating Two-Leg Ladder
Dimerized spin-1/2 ladders exhibit a variety of phase structures, which depend on the intra-chain and inter-chain spin exchange energies as well as on the dimerization pattern of the ladder. Using the density matrix renormalization group (DMRG) algorithm, we study critical properties of the bond-alternating two-leg Heisenberg spin ladder with diagonal interaction J ×. Two types of spin systems, staggered dimerized antiferromagnetic ladder and columnar dimerized ferro-antiferromagnetic couplings ladder, are investigated. To clarify the phase transition behaviors, we simultaneously analyze the string order parameter (SOP), the twisted order parameter (TOP), as well as a measurement of the quantum information analysis. Based on measuring this different observables, we establish the phase diagram accurately and give the fitting functions of the phase boundaries. In addition, the phase transition of cross-coupled spin ladder (in the absence of intrinsic dimerization) is also discussed.
We investigate the ground-state phase diagram of the S=12\mathrm{S}=\frac{1}{2}S=21​ two-leg XXZXXZXXZ spin-ladder system with an isotropic interchain coupling. In this model, there is the Berezinskii-Kosterlitz-Thouless transition which occurs at the XYXYXY-Haldane and XYXYXY-rung singlet phase boundaries. It was difficult to determine the transition line using traditional methods. We overcome this difficulty using the level spectroscopy method combined with the twisted boundary condition method, and we check the consistency. We find out that the phase boundary between XYXYXY phase and Haldane phase lies on $\ensuremath{\Delta}=0$ line. And we show that there exist two different XYXYXY phases, which we can distinguish investigating a XXXXXX correlation function.
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