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.
The goal of this project is to study the ground-state properties of frustrated spin-1/2 two- and three-leg Heisenberg ladders, and to investigate possible effects of diagonal couplings on spin gaps. The ground-state and the first-excited-state energies of these two systems are calculated systematically by using the density matrix renormalization group method. The ground state phase diagrams for these two systems are obtained. For the frustrated two-leg ladder, we found that the spin gap is insensitive to the change of the FM diagonal coupling constant. This is in agreement with experimental suggestions. For the frustrated three-leg ladder, we conclusively proved that introducing AF diagonal couplings can not change the gapless property of the ground state.
We consider a two-leg ladder system with interactions varying from constant rung coupling to systematic diminishing of rung interactions leading to diverging chains. We compare and contrast their ground state and excitation characteristics using density matrix renormalization group methods. We find that the finite spin gap in a constant coupling ladder develops into a gapless excitation with slight diminishing of the distance dependent coupling. Varying the spatial range of the rung coupling, we derive the effective length scale of triplet excitations in these ladder classes of systems.
The low-energy effective Hamiltonian of three coupled spin chains with periodic boundary conditions (spin tube) is expressed, in the limit of strong interchain coupling, in terms of
XXZ chains coupled by biquadratic exchange interaction. A similar effective model was also proposed to describe the coupling of spins to orbital degrees of freedom in materials such as
NaV2O5. We investigate the effective model by means of bosonization and renormalization-group techniques, and find that the generic phase diagram comprises a gapless region and gapped regions consisting of a spin liquid phase and various antiferromagnetic phases. We discuss the properties of the spin liquid phase, in particular the nature of the ground state and of the elementary excitations above it. We then study the effect of a magnetic field, and conclude that a strong enough magnetic field can suppress the dimerized phase leading to a two component Luttinger liquid. The critical exponents at the gapful-gapless transition are calculated and shown to be nonuniversal in the spin-tube case or the generic spin- orbital problem.
Using the density matrix renormalization group method we have studied the ground-state phase diagram of a spin-1/2 frustrated three-leg antiferromagnetic Heisenberg ladder, and identified two phases corresponding to the spin-3/2 chain and the standard spin ladder. Varying the diagonal coupling ${J}_{\ifmmode\times\else\texttimes\fi{}}$ leads to a quantum phase transition from one ground state to the other, but does not alter the gapless nature of the excitation spectra. On the phase boundary, the degenerate ground states form a chiral spin liquid with a central charge
c=2. The critical value of ${J}_{\ifmmode\times\else\texttimes\fi{}}$ is insensitive to the number of legs in the ladder, suggesting that a quantum phase transition may occur at ${J}_{\ifmmode\times\else\texttimes\fi{}}=0.6$ for the isotropic spin-1/2 antiferromagnetic Heisenberg model on the square lattice.