Heisenberg spin chain with random-sign couplings

We study the 1D quantum Heisenberg chain with randomly ferromagnetic or antiferromagnetic couplings (a model previously studied by approximate strong-disorder RG). We find that, at least for sufficiently large spin $S$, the ground state has ``spin glass’’ order. The spin waves on top of this state have the dynamical exponent $z=3\mathrm{/}2$, intermediate between the values $z=1$ of the antiferromagnet and $z=2$ of the ferromagnet. DMRG simulations are in good agreement with the analytical results for spins $S=1$ and $S=3\mathrm{/}2$. The case $S=1\mathrm{/}2$ shows large finite size effects: we suggest that this case is also ordered, but with a small ordered moment.