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arXiv:cond-mat/9910103 · Physical review. B, Condensed matter

Phase diagram of ferrimagnetic ladders with bond alternation

A. Langari, Ramin Abolfath, Miguel Angel Martin-Delgado

Published Jan 1, 2000• 23 citations
arXivHTMLPDF

Abstract

We study the phase diagram of a two-leg bond-alternation spin-(1/2, 1) ladder for two different configurations using a quantum renormalization-group approach. Although d-dimensional ferrimagnets show gapless behavior, we will explicitly show that the effect of the spin mixing and the bond alternation can open the possibility for observing an energy gap. We show that the gapless phases of such systems can be equivalent to the one-dimensional half-integer antiferromagnets, besides the gapless ferrimagnetic phases. We therefore propose a phase transition between these two gapless phases that can be seen in the parameter space.

DOI
10.1103/physrevb.61.343

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We study the phase diagram of a two-leg bond-alternation spin-(1/2, 1) ladder for two different configurations using a quantum renormalization-group approach. Although d-dimensional ferrimagnets show gapless behavior, we will explicitly show that the effect of the spin mixing and the bond alternation can open the possibility for observing an energy gap. We show that the gapless phases of such systems can be equivalent to the one-dimensional half-integer antiferromagnets, besides the gapless ferrimagnetic phases. We therefore propose a phase transition between these two gapless phases that can be seen in the parameter space.
We apply the Lanczos method to a two-leg ladder with mixed spins of magnitudes (S1,S2)=(1,1/2){(S}_{1}{,S}_{2})=(1,1/2)(S1​,S2​)=(1,1/2) located at alternating positions along the ladder. The effect of dimerization $\ensuremath{\gamma}$ is also considered according to two different patterns. A spin-wave theory (SWT) is applied to this model predicting one gapless branch with ferromagnetic properties and another gapful branch with antiferromagnetic nature as low-energy excitations of the model. We compute the ground-state energies, ferromagnetic and antiferromagnetic excitation gaps, magnetizations, and correlation functions as a function of ${J}^{\ensuremath{'}}$ and $\ensuremath{\gamma}$ which results into a fine estimate of the phase diagram. The Lanczos results are compared with the SWT analysis and a qualitative agreement is found but with numerical discrepancies. We also study numerically the spin-Peierls instability and find that it is conditional for any value of ${J}^{\ensuremath{'}}\ensuremath{\in}(0,2)$ and both dimerization patterns.
Using the density matrix renormalization group method, we determine the phase diagram of a frustrated bond-alternating S = 1/2 Heisenberg ladder with ferro-antiferromagnetic couplings at zero temperature. With the interactions between spins along the rungs set, we identify three spin-gapped phases (the Haldane phase, the singlet phase and the dimer phase) in the whole parameter range. The analysis of our data shows that two-leg spin bond-alternating ladders have a rich phase diagram if both rung and diagonal couplings are taken into account.
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 study the impact of the diagonal frustrating couplings on the quantum phase diagram of a two-leg ladder composed of alternating spin-1 and spin-12\frac{1}{2}21​ rungs. As the coupling strength is increased the system successively exhibits two gapped paramagnetic phases (a rung-singlet and a Haldane-type nondegenerate states) and two ferrimagnetic phases with different ferromagnetic moments per rung. The first two states are similar to the phases studied in the frustrated spin-12\frac{1}{2}21​ ladder, whereas the magnetic phases appear as a result of the mixed-spin structure of the model. A detailed characterization of these phases is presented using density-matrix renormalization-group calculations, exact diagonalizations of periodic clusters, and an effective Hamiltonian approach inspired by the analysis of numerical data. The present theoretical study was motivated by the recent synthesis of the quasi-one-dimensional ferrimagnetic material FeIIFeIII{\text{Fe}}^{\text{II}}{\text{Fe}}^{\text{III}}FeIIFeIII (trans-1,4-cyclohexanedicarboxylate) exhibiting a similar ladder structure.
Phase Diagram of the Spin-12\frac{1}{2}21​ Bond-Alternating Two-Leg Ladder
The ground-state phase diagram of a Heisenberg $\text{spin}\ensuremath{-}\frac{1}{2}$ system on a two-leg ladder with rung alternation is studied by combining analytical approaches with numerical simulations. For the case of ferromagnetic leg exchanges a unique ferrimagnetic ground state emerges, whereas for the case of antiferromagnetic leg exchanges several different ground states are stabilized depending on the ratio between exchanges along legs and rungs. For the more general case of a honeycomb-ladder model for the case of ferromagnetic leg exchanges besides the usual rung-singlet and saturated ferromagnetic states we obtain a ferrimagnetic Luttinger liquid phase with both linear and quadratic low-energy dispersions and ground-state magnetization continuously changing with system parameters. For the case of antiferromagnetic exchanges along legs, different dimerized states including states with additional topological order are suggested to be realized.