We show how the low energy properties of the two-leg XXZ spin-1/2 ladders with general anisotropy parameter Δ on closed geometries can be accounted for in the framework of the m -reduction procedure developed previously (Cristofano et al 2000 Mod. Phys. Lett. A 15 547; Cristofano et al 2000 Mod. Phys. Lett. A 15 1679; Cristofano et al 2002 Nucl. Phys. B 641 547; Cristofano et al 2004 J. High Energy Phys. JHEP06(2004) 056). In the limit of quasi-decoupled chains, a conformal field theory (CFT) with central charge c = 2 is derived and its ability to describe the model with different boundary conditions is shown. Special emphasis is given to the Mobius boundary conditions which generate a topological defect corresponding to non-trivial single-spinon excitations. Then, in the case of the two-leg XXX ladders we discuss in detail the role of various perturbations in determining the renormalization group flow starting from the ultraviolet (UV) critical point with c = 2.
Heisenberg antiferromagnetic spin ``ladders'' (two coupled spin chains) are low-dimensional magnetic systems which for S=1/2 interpolate between half-integer-spin chains, when the chains are decoupled, and effective integer-spin one-dimensional chains in the strong-coupling limit. The spin-1/2 ladder may be realized in nature by vanadyl pyrophosphate, (VO
)2P2O7. In this paper we apply strong-coupling perturbation theory, spin-wave theory, Lanczos techniques, and a Monte Carlo method to determine the ground-state energy and the low-lying excitation spectrum of the ladder. We find evidence of a nonzero spin gap for all interchain couplings ${\mathit{J}}_{\mathrm{\ensuremath{\perp}}}$>0. A band of spin-triplet excitations above the gap is also analyzed. These excitations are unusual for an antiferromagnet, since their long-wavelength dispersion relation behaves as (k-
k0)2 (in the strong-coupling limit ${\mathit{J}}_{\mathrm{\ensuremath{\perp}}}$\ensuremath{\gg}J, where J is the in-chain antiferromagnetic coupling). Their band is folded, with a minimum energy at
k0=\ensuremath{\pi}, and a maximum between
k1=\ensuremath{\pi}/2 (for ${\mathit{J}}_{\mathrm{\ensuremath{\perp}}}$=0) and 0 (for ${\mathit{J}}_{\mathrm{\ensuremath{\perp}}}$=\ensuremath{\infty}). We also give numerical results for the dynamical structure factor S(q,\ensuremath{\omega}), which can be determined in neutron scattering experiments. Finally, possible experimental techniques for studying the excitation spectrum are discussed.
We study the zero-temperature magnetization process $(M\ensuremath{-}H$ curve) of one-dimensional quantum antiferromagnets using a variant of the density-matrix renormalization group method. For both the
S=1/2 zig-zag spin ladder and the
S=1 bilinear-biquadratic chain, we find clear cusp-type singularities in the middle-field region of the $M\ensuremath{-}H$ curve. These singularities are successfully explained in terms of the double-minimum shape of the energy dispersion of the low-lying excitations. For the
S=1/2 zig-zag spin ladder, we find that the cusp formation accompanies the Fermi-liquid to non-Fermi-liquid transition.
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 study ground-state properties and the low-lying excitations of Heisenberg spin ladders composed of two ferrimagnetic chains with alternating site spins
(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=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.
We study the ground state and low-lying excited states of the Kitaev-Heisenberg model on a two-leg ladder geometry using the density-matrix renormalization-group and Lanczos exact diagonalization methods. The Kitaev and Heisenberg interactions are parametrized as $K=sin\ensuremath{\phi}$ and $J=cos\ensuremath{\phi}$ with an angle parameter $\ensuremath{\phi}$. Based on the results for several types of order parameters, excitation gaps, string order parameter, and entanglement spectra, the $\ensuremath{\phi}$-dependent ground state phase diagram is determined. Remarkably, the phase diagram is quite similar to that of the Kitaev-Heisenberg model on a honeycomb lattice, exhibiting the same long-range-ordered states, namely rung singlet (analog to N\'eel in three dimensions), zigzag, ferromagnetic, and stripy, and the presence of gapped spin liquids around the exactly solvable Kitaev points $\ensuremath{\phi}=\ifmmode\pm\else\textpm\fi{}\ensuremath{\pi}/2$. We also calculate the expectation value of a plaquette operator corresponding to a $\ensuremath{\pi}$-flux state in order to establish how the gapped Kitaev spin liquid extends away from the $\ensuremath{\phi}=\ifmmode\pm\else\textpm\fi{}\ensuremath{\pi}/2$. Furthermore, we determine the dynamical spin structure factor and discuss the effect of the Kitaev interaction on the spin-triplet dispersion.