We consider a spin-1/2 ladder with a ferromagnetic rung coupling J perpendicular and inequivalent chains. This model is obtained by a twist (theta) deformation of the ladder and interpolates between the isotropic ladder (theta=0) and the SU(2) ferromagnetic Kondo necklace model (theta = pi). We show that the ground state in the (theta, J perpendicular) plane has a finite string order parameter characterizing the Haldane phase. Twisting the chain introduces a new energy scale, which we interpret in terms of a Suhl-Nakamura interaction. As a consequence we observe a crossover in the scaling of the spin gap at weak coupling from delta/J parallel proportional, variant J perpendicular/J parallel for theta < theta c approximately 8 pi/9 to delta/J parallel proportional, variant (J perpendicular/J parallel)2 for theta > theta c. Those results are obtained on the basis of large scale quantum Monte Carlo calculations.

We consider asymmetric spin-1 2 two-leg ladders with nonequal antiferromagnetic ͑AF͒ couplings J ʈ and J ʈ along legs ͑ Յ 1͒ and ferromagnetic rung coupling, J Ќ . This model is characterized by a gap ⌬ in the spectrum of spin excitations. We show that in the large J Ќ limit this gap is equivalent to the Haldane gap for the AF spin-1 chain, irrespective of the asymmetry of the ladder. The behavior of the gap at small rung coupling falls in two different universality classes. The first class, which is best understood from the case of the conventional symmetric ladder at = 1, admits a linear scaling for the spin gap ⌬ ϳ J Ќ . The second class appears for a strong asymmetry of the coupling along legs, J ʈ Ӷ J Ќ Ӷ J ʈ and is characterized by two energy scales: the exponentially small spin gap ⌬ ϳ J Ќ exp͑−J ʈ / J Ќ ͒, and the bandwidth of the low-lying excitations induced by a Suhl-Nakamura indirect exchange ϳJ Ќ 2 / J ʈ . We report numerical results obtained by exact diagonalization, densitymatrix renormalization group and quantum Monte Carlo simulations for the spin gap and various spin correlation functions. Our data indicate that the behavior of the string order parameter, characterizing the hidden AF order in Haldane phase, is different in the limiting cases of weak and strong asymmetries. On the basis of the numerical data, we propose a low-energy theory of effective spin-1 variables, pertaining to large blocks on a decimated lattice.

We study single hole dynamics in the bilayer Heisenberg and Kondo Necklace models. Those models exhibit a magnetic order-disorder quantum phase transition as a function of the interlayer coupling J ⊥ . At strong coupling in the disordered phase, both models have a single-hole dispersion relation with band maximum at p p p = (π, π) and an effective mass at this p p p−point which scales as the hopping matrix element t. In the Kondo Necklace model, we show that the effective mass at p p p = (π, π) remains finite for all considered values of J ⊥ such that the strong coupling features of the dispersion relation are apparent down to weak coupling. In contrast, in the bilayer Heisenberg model, the effective mass diverges at a finite value of J ⊥ . This divergence of the effective mass is unrelated to the magnetic quantum phase transition and at weak coupling the dispersion relation maps onto that of a single hole doped in a planar antiferromagnet with band maximum at p p p = (π/2, π/2). We equally study the behavior of the quasiparticle residue in the vicinity of the magnetic quantum phase transition both for a mobile and static hole. In contrast to analytical approaches, our numerical results do not unambiguously support the fact that the quasiparticle residue of the static hole vanishes in the vicinity of the critical point. The above results are obtained with a generalized version of the loop algorithm to include single hole dynamics on lattice sizes up to 20 × 20.

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