Translational symmetry breaking in two-dimensional antiferromagnets and superconductors

It was argued many years ago that translational symmetry breaking due to th e appearance of spin-Peierls ordering (or bond-charge stripe order) is a fu ndamental property of the quantum paramagnetic states of a large class of s quare lattice antiferromagnets. Recently, such states were shown to be a co nvenient point of departure for studying translational symmetry breaking in doped antiferromagnets: these results are briefly reviewed here with an em phasis on experimental implications. In the presence of stronger frustratio n, it was also argued that the insulating antiferromagnet can undergo a tra nsition to a deconfined state with no lattice symmetry breaking. This trans ition is described by a fully-frustrated Ising model in a transverse field: details of this earlier derivation of the Ising model are provided here-th is is motivated by the reappearance of the same Ising model in a recent stu dy of the competition between antiferromagnetism and d-wave superconductivi ty by Senthil and Fisher.