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Plaquette Order in a Dimerized Frustrated Spin-Ladder

We study the effect of spin-Peierls instability on the phase-diagram of a frustrated antiferromagnetic spin-1/2 ladder, with weak transverse and diagonal rung coupling. Our analysis focuses on a one-dimensional version of the model (i.e. a single two-leg ladder) where we consider two forms of spin-Peierls (SP) instabilities on the legs: columnar dimers (CD) and staggered dimers (SD). We particularly examine the regime of parameters (corresponding to an intermediate XXZ anisotropy) where the SP and rung coupling terms are equally relevant. In both the CD and SD cases we find that the effective field theory describing the system is a self-dual sine-Gordon model, which favors ordering and the opening of a gap to excitations. The order parameter, which reflects the interplay between the SP and rung interactions, represents a crystal of 4-spin plaquettes on which longitudinal and transverse dimers are in a superposition. Depending on the SP instability mode these plaquettes are closed or open, however both types spontaneously break reflection symmetry across the ladder. The closed plaquettes are stable, while the open plaquette-order is relatively fragile and the corresponding gap may be tuned to zero under extreme conditions. We further find that a first order transition occurs from the Plaquette order to a valence bond crystal (VBC) of dimers on the legs. It is suggestive that in a higher dimensional version of this system, this variety of distinct VBC states with comparable energies leads to the formation of domains. Effectively one-dimensional gapless spinon modes on domain boundaries can possibly account for the experimental observation of a spin-liquid behavior in a physical realization of the model.