Heisenberg spin chain with random-sign couplings

Abstract

We study the 1D quantum Heisenberg chain with randomly ferromagnetic or antiferromagnetic couplings [a model previously studied by approximate strong-disorder renormalization group (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 / 2 , intermediate between the values z = 1 of the antiferromagnet and z = 2 of the ferromagnet. Density matrix renormalization group (DMRG) simulations are in good agreement with the analytical results for spins S = 1 and S = 3 / 2 . The case S = 1 / 2 shows large finite size effects: We suggest that this case is also ordered, but with a small ordered moment.