  It was argued many years ago that translational symmetry breaking due to the
appearance of spin-Peierls ordering (or bond-charge stripe order) is a
fundamental property of the quantum paramagnetic states of a large class of
square lattice antiferromagnets. Recently, such states were shown to be a
convenient point of departure for studying translational symmetry breaking in
doped antiferromagnets: these results are briefly reviewed here with an
emphasis on experimental implications. In the presence of stronger frustration,
it was also argued that the insulating antiferromagnet can undergo a transition
to a deconfined state with no lattice symmetry breaking. This transition is
described by a fully-frustrated Ising model in a transverse field: details of
this earlier derivation of the Ising model are provided here--this is motivated
by the reappearance of the same Ising model in a recent study of the
competition between antiferromagnetism and d-wave superconductivity by Senthil
and Fisher (cond-mat/9910224).
