We use exact diagonalization and the modified Lanczos method to study the finite-energy and finite-momentum spectral weight of the longitudinal and transverse spin excitations of the anisotropic zig-zag ladder. We find that the spin excitations form continua of gapless or gapped spinons in the different regions of the phase diagram. The results obtained are consistent with a picture previously proposed that in the anisotropic case there is a transition from a gapped regime to a gapless regime, for small interchain coupling. In the gapless regime we find a sharp low-energy peak in the structure function for the transverse spin excitations, consistent with a finite stiffness.
We analyze an anisotropic spin-1/2 two-leg ladder in the presence of various types of random perturbations. The generic phase diagram for the pure system, in a way similar to spin one chains, consists of four phases: an antiferromagnet, a Haldane gap or a singlet phase (depending on the sign of interchain coupling), and two
XY phases designated by
XY1 and
XY2. The effects of disorder depend crucially on whether it preserves
XY symmetry (random field along
z and random exchange) or not (random anisotropy or random
XY fields). In all cases we computed the new phase diagram and the correlation length for the disordered system. The ladder exhibits a remarkable stability to disorder with
XY symmetry. Not only the singlet phases but also the massless
XY1 phase are totally unaffected by disorder in stark contrast with the single chain case. Even in the presence of an external magnetic field breaking the spin gap most of the phase diagram (including the
XY point) remains unaffected by the disorder, again in opposition with the single chain case. This stabilization towards disorder is similar, albeit stronger, to the one occurring for fermionic ladders. On the other hand, the
XY2 phase is very strongly suppressed. Disorder breaking
XY symmetry has much stronger effects and most of the phases at the exception of the singlet one are now destroyed. Interestingly, the disordered
XY1 phase has a much shorter correlation length than the disordered
XY2 phase contrarily with the case of perturbations preserving the rotation symmetry around the
z axis. The ladder system is thus in fact much more anisotropic than its single chain counterpart with identical exchanges. Finally we examine the case of strong disorder or weak interchain exchange for
XY symmetric disorder. Close to the isotropic point, when the interchain exchange is increased the system undergoes a transition between two decoupled disordered spin-1/2 chains to a singlet ladder unaffected by disorder. For more
XY like systems, the transition occurs in two steps with a nondisordered
XY1 phase occurring between the decoupled chains and the singlet phase. Comparison with other disordered gapped systems such as spin one chains is discussed.
We analyze the phase diagram of a system of spin-1/2 Heisenberg antiferromagnetic chains interacting through a zig-zag coupling, also called zig-zag ladders. Using bosonization techniques we study how a spin-gap or more generally plateaux in magnetization curves arise in different situations. While for coupled XXZ chains, one has to deal with a recently discovered chiral perturbation, the coupling term which is present for normal ladders is restored by an external magnetic field, dimerization or the presence of charge carriers. We then proceed with a numerical investigation of the phase diagram of two coupled Heisenberg chains in the presence of a magnetic field. Unusual behaviour is found for ferromagnetic coupled antiferromagnetic chains. Finally, for three (and more) legs one can choose different inequivalent types of coupling between the chains. We find that the three-leg ladder can exhibit a spin-gap and/or non-trivial plateaux in the magnetization curve whose appearance strongly depends on the choice of coupling.
We investigate the effect of dimensional crossover in the ground state of the antiferromagnetic spin-1 Heisenberg model on the anisotropic triangular lattice that interpolates between the regime of weakly coupled Haldane chains $({J}^{\ensuremath{'}}\ensuremath{\ll}J)$ and the isotropic triangular lattice $({J}^{\ensuremath{'}}=J)$. We use the density-matrix renormalization group (DMRG) and Schwinger boson theory performed at the Gaussian correction level above the saddle-point solution. Our DMRG results show an abrupt transition between decoupled spin chains and the spirally ordered regime at ${({J}^{\ensuremath{'}}/J)}_{c}\ensuremath{\sim}0.42$, signaled by the sudden closing of the spin gap. Coming from the magnetically ordered side, the computation of the spin stiffness within Schwinger boson theory predicts the instability of the spiral magnetic order toward a magnetically disordered phase with one-dimensional features at ${({J}^{\ensuremath{'}}/J)}_{c}\ensuremath{\sim}0.43$. The agreement of these complementary methods, along with the strong difference found between the intra- and the interchain DMRG short spin-spin correlations for sufficiently large values of the interchain coupling, suggests that the interplay between the quantum fluctuations and the dimensional crossover effects gives rise to the one-dimensionalization phenomenon in this frustrated spin-1 Hamiltonian.
The phase diagram of a frustrated spin-S zig-zag ladder is studied through different numerical and analytical methods. We show that for arbitrary S, there is a family of Hamiltonians for which a fully-dimerized state is an exact ground state, being the Majumdar-Ghosh point for a particular member of the family. We show that the system presents a transition between a dimerized phase to a Néel-like phase for S = 1/2, and spiral phases can appear for large S. The phase diagram is characterized by means of a generalization of the usual mean field approximation. The novelty in the present implementation is to consider the strongest coupled sites as the unit cell. The gap and the excitation spectrum is analyzed through the random phase approximation. Also, a perturbative treatment to obtain the critical points is discussed. Comparisons of the results with numerical methods like the Density Matrix Renormalization Group are also presented.
We investigate the spatially anisotropic square lattice quantum antiferromagnet. The model describes isotropic spin-1/2 Heisenberg chains (exchange constant J) coupled antiferromagnetically in the transverse (J( perpendicular )) and diagonal (J(x)), with respect to the chain, directions. Classically, the model admits two ordered ground states-with antiferromagnetic and ferromagnetic interchain spin correlations-separated by a first-order phase transition at J( perpendicular )=2J(x). We show that in the quantum model this transition splits into two, revealing an intermediate quantum-disordered columnar dimer phase, both in two dimensions and in a simpler two-leg ladder version. We describe quantum-critical points separating this spontaneously dimerized phase from classical ones.