6 research outputs found
Decoupling of the S=1/2 antiferromagnetic zig-zag ladder with anisotropy
The spin-1/2 antiferromagnetic zig-zag ladder is studied by exact
diagonalization of small systems in the regime of weak inter-chain coupling. A
gapless phase with quasi long-range spiral correlations has been predicted to
occur in this regime if easy-plane (XY) anisotropy is present. We find in
general that the finite zig-zag ladder shows three phases: a gapless collinear
phase, a dimer phase and a spiral phase. We study the level crossings of the
spectrum,the dimer correlation function, the structure factor and the spin
stiffness within these phases, as well as at the transition points. As the
inter-chain coupling decreases we observe a transition in the anisotropic XY
case from a phase with a gap to a gapless phase that is best described by two
decoupled antiferromagnetic chains. The isotropic and the anisotropic XY cases
are found to be qualitatively the same, however, in the regime of weak
inter-chain coupling for the small systems studied here. We attribute this to a
finite-size effect in the isotropic zig-zag case that results from
exponentially diverging antiferromagnetic correlations in the weak-coupling
limit.Comment: to appear in Physical Review
The spin-1/2 J1-J2 Heisenberg antiferromagnet on the square lattice: Exact diagonalization for N=40 spins
We present numerical exact results for the ground state and the low-lying
excitations for the spin-1/2 J1-J2 Heisenberg antiferromagnet on finite square
lattices of up to N=40 sites. Using finite-size extrapolation we determine the
ground-state energy, the magnetic order parameters, the spin gap, the uniform
susceptibility, as well as the spin-wave velocity and the spin stiffness as
functions of the frustration parameter J2/J1. In agreement with the generally
excepted scenario we find semiclassical magnetically ordered phases for J2 <
J2^{c1} and J2 > J2^{c2} separated by a gapful quantum paramagnetic phase. We
estimate J2^{c1} \approx 0.35J1 and J2^{c2} \approx 0.66J1.Comment: 16 pages, 2 tables, 11 figure