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The influence of the Hubbard interaction on the lattice structure of two half-filled Su-Shrieffer-Heeger chains coupled by constant electron hoppings is examined using a linked cluster expansion of the Gutzwiller variational wave function as well as second-order perturbation theory. Parallel and antiparallel dimerized crystal structures are considered. In the uncorrelated system the metallic undimerized and the insulating parallel dimerized phase compete. However, the state of lowest energy is antiparallel dimerized. In the case of finite Hubbard interaction both the variational and the perturbational approach yield a stabilization of the parallel dimerized configuration. For the parallel dimerized model, the Gutzwiller ansatz signals a new ordering of the electrons in the bands: holes are present in the highest occupied single-particle states; the upper valence band is occupied and the lower conduction band is empty even in the 'metallic' phase characterized by crossing bands.

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