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arXiv:cond-mat/0012209 · Physical review. B, Condensed matter

Low-energy properties of ferrimagnetic two-leg ladders: A Lanczos study

A. Langari, Miguel Angel Martin-Delgado

Published Jan 12, 2001• 13 citations
arXivHTMLPDF

Abstract

We apply the Lanczos method to a two-leg ladder with mixed spins of magnitudes ${(S}_{1}{,S}_{2})=(1,1/2)$ 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.

DOI
10.1103/physrevb.63.054432

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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 \ensuremathγ\ensuremath{\gamma}\ensuremathγ 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′{J}^{\ensuremath{'}}J\ensuremath′ and \ensuremathγ\ensuremath{\gamma}\ensuremathγ 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∈(0,2){J}^{\ensuremath{'}}\ensuremath{\in}(0,2)J\ensuremath′\ensuremath∈(0,2) and both dimerization patterns.
We study numerically the formation of magnetization plateaux with the Lanczos method in two-leg ladders 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 and with dimerization $\ensuremath{\gamma}.$ For interchain coupling ${J}^{\ensuremath{'}}>0$ and $\ensuremath{\gamma}=0,$ we find normalized plateaux at m=1/3m=1/3m=1/3 starting at zero field and m=1m=1m=1 (saturation), while when $\ensuremath{\gamma}\ensuremath{\ne}0$ is columnar, another extra plateau at m=2/3m=2/3m=2/3 shows up. For ${J}^{\ensuremath{'}}<0,$ when $\ensuremath{\gamma}<{\ensuremath{\gamma}}_{c}{(J}^{\ensuremath{'}})$ we find no plateau while for $\ensuremath{\gamma}>{\ensuremath{\gamma}}_{c}{(J}^{\ensuremath{'}})$ we find four plateaux at m=0,1/3,2/3,1.m=0,1/3,2/3,1.m=0,1/3,2/3,1. We also apply several approximate analytical methods (spin-wave theory, low-energy effective Hamiltonians, and bosonization) to understand these findings and to conjecture the behavior of ferrimagnetic ladders with a larger number of legs.
We study ground-state properties and the low-lying excitations of Heisenberg spin ladders composed of two ferrimagnetic chains with alternating site spins (S1>S2){(S}_{1}>{S}_{2})(S1​>S2​) by using the bosonic Dyson-Maleev formalism and Lanczos numerical techniques. The emphasis is on properties of the ferrimagnetic phase, which is stable for antiferromagnetic interchain couplings ${J}_{\ensuremath{\perp}}>~0$. There are two basic implications of the underlying lattice structure: (i) the spin-wave excitations form folded acoustic and optical branches in the extended Brillouin zone and (ii) the ground-state parameters (such as the on-site magnetizations and spin-stiffness constant) show a crossover behavior in the weak-coupling region $0<{J}_{\ensuremath{\perp}}<1$. The above peculiarities of the ladder ferrimagnetic state are studied up to second order in the quasiparticle interaction and by a numerical diagonalization of ladders containing up to N=12N=12N=12 rungs. The presented results for the ground-state parameters and the excitation spectrum can be used in studies on the low-temperature thermodynamics of ferrimagnetic ladders.
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.
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.
The energy spectra and low-temperature magnetic properties of two one-dimensional Heisenberg mixed spin (s = 1, 1/2) systems, namely decorated two-leg mixed spin ladders with the lattice topology of polyacene, are studied. The gapless character of the exact excitation energy spectra for both ladder models has been determined. We found numerically that the model with macroscopic ground state spin S0 has gapped excitations with the spin S > S0. This leads to the appearance of an intermediate plateau in field dependence of magnetization at low temperatures. We have shown that the ladder with equal coupling in legs has the maximal size of this plateau at the same coupling in rungs. For a mixed spin ladder model with Ising interactions in legs, the appearance of two intermediate magnetization plateaus at low temperatures and some values of coupling parameters was shown.
Using the density matrix renormalization group method, we have obtained the ground-state phase diagram of a spin-1/2 two-leg antiferromagnetic Heisenberg ladder with a ferromagnetic diagonal interaction ${J}_{\ifmmode\times\else\texttimes\fi{}}.$ The boundary between the two phases found in the system, the Haldane phase and the singlet phase, lies in the frustrated area of the parameter space, i.e., both the rung coupling ${J}_{\ensuremath{\perp}}$ and the diagonal coupling ${J}_{\ifmmode\times\else\texttimes\fi{}}$ are ferromagnetic. The spin gap is found to be insensitive to the change of the ferromagnetic diagonal coupling strength when the ratio of the rung coupling constant ${J}_{\ensuremath{\perp}}$ to the leg coupling constant ${J}_{\ensuremath{\Vert}}$ is 0.5, in agreement with the analysis of recent experimental spin susceptibility data.