  Studies of competing orders in 1D magnetic chains have attracted considerable
attention in recent years, as the presence of long-range Heisenberg
interactions is found to allow interesting quantum phase transitions. We
investigate here the role of spin-orbit effects by considering spin-1/2 chains
in the presence of both collinear and non-collinear long-range interactions. By
employing exact diagonalization and density matrix renormalization group
calculations we investigate the rich phase diagram of this system. We find
transitions from collinear to transverse magnetic correlated order as the
strength of the non-collinear coupling increases, accompanied by a jump in the
vector spin chirality order parameter of the system. This shows that tuning
long-range interactions allows control of the onset of sizable vector spin
chirality in a system, which may be used to transmit information down the
chain. We investigate the characteristic structure of the distinct phases and
explore their possible physical implementation in different materials systems.
