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arXiv:cond-mat/9809032 · Physical review. B, Condensed matter

Phase diagram of magnetic ladders constructed from a composite-spin model

Örs Legeza, Gábor Fáth, Jenő Sólyom

Published Jan 1, 1997• 31 citations
arXivHTMLPDF

Abstract

White's density matrix renormalization group method has been applied to an S=1/2+1/2 composite-spin model, which can also be considered as a two-leg ladder model. By appropriate choices of the coupling constants this model allows one not only to study how the gap is opened around the gapless integrable models, but also to interpolate continuously between models with different spin lengths. We have found indications for the existence of several different massive phases.

DOI
10.1103/physrevb.55.291

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White's density matrix renormalization group method has been applied to an S=1/2+1/2 composite-spin model, which can also be considered as a two-leg ladder model. By appropriate choices of the coupling constants this model allows one not only to study how the gap is opened around the gapless integrable models, but also to interpolate continuously between models with different spin lengths. We have found indications for the existence of several different massive phases.
We have considered the properties of anisotropic two-leg ladder models with S=1/2S=1/2S=1/2 or S=1S=1S=1 spins on the rungs, using White's density-matrix renormalization-group method. We have generalized the method by taking into account the symmetries of the model in order to reduce the dimensions of the matrix to be diagonalized, thereby making it possible to consider more states. The boundaries in the parameter space of the extended region, where the Haldane phase exists, are estimated.
We investigate an asymmetric zigzag spin ladder with different exchange integrals on both legs using bosonization and renormalization group approaches. When the leg exchange integrals and frustration both are sufficiently small, renormalization group analysis shows that the Heisenberg critical point flows to an intermediate-coupling fixed point with gapless excitations and a vanishing spin velocity. When they are large, a spin gap opens and a dimer liquid is realized. Here, we find a continuous manifold of Hamiltonians with dimer product ground states, interpolating between the Majumdar-Ghosh and sawtooth spin-chain model.
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.
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 investigate the NNN-leg spin-SSS Heisenberg ladders by using the density matrix renormalization group method. We present estimates of the spin gap ${\ensuremath{\Delta}}_{s}$ and of the ground-state energy per site ${e}_{\ensuremath{\infty}}^{N}$ in the thermodynamic limit for ladders with widths up to six legs and spin $S\ensuremath{\le}\frac{5}{2}$. We also estimate the ground-state energy per site ${e}_{\ensuremath{\infty}}^{2\mathrm{D}}$ for the infinite two-dimensional spin-SSS Heisenberg model. Our results support that for ladders with semi-integer spins the spin excitation is gapless for NNN odd and gapped for NNN even, whereas for integer spin ladders the spin gap is nonzero, independent of the number of legs. Those results agree with the well-known conjectures of Haldane and S\'en\'echal-Sierra for chains and ladders, respectively. We also observe edge states for ladders with NNN odd, similar to what happens in spin chains.
A large variety of materials can be approximately described by means of spin-1/2 Heisenberg ladders. Here, the Density Matrix Renormalization Group (DMRG) algorithm together with a previously established numerical self-consistent mean-field approximation is used to investigate the magnetic properties of spin ladders coupled in a second dimension. The full ground state phase diagram including spin-gapped, antiferromagnetic, ferrimagnetic and fully polarized phases is presented as a function of interladder and intraladder coupling and magnetic field. Measurement of the dependence of magnetization on applied magnetic field is shown to enable location of a material on the phase diagram and determination of the Hamiltonian parameters. These results provide a practical route toward identifying and characterizing magnetic materials composed of coupled spin ladders.