  We demonstrate in theory that it is possible to all-electrically manipulate
the RKKY interaction in a quasi-one-dimensional electron gas embedded in a
semiconductor heterostructure, in the presence of Rashba and Dresselhaus
spin-orbit interaction. In an undoped semiconductor quantum wire where
intermediate excitations are gapped, the interaction becomes the short-ranged
Bloembergen-Rowland super-exchange interaction. Owing to the interplay of
different types of spin-orbit interaction, the interaction can be controlled to
realize various spin models, e.g., isotropic and anisotropic Heisenberg-like
models, Ising-like models with additional Dzyaloshinsky-Moriya terms, by tuning
the external electric field and designing the crystallographic directions. Such
controllable interaction forms a basis for quantum computing with localized
spins and quantum matters in spin lattices.
