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We study a model of strongly correlated S=1/2 fermions on the planarpyrochlore, or checkerboard, lattice, at fractional (1/8) filling. Startingwith the extended Hubbard model in the limit of strong Coulomb repulsion,low-energy configurations can be mapped onto hard-core dimer configurationswhose dimers carry a spin degree of freedom. An effective Hamiltonian similarto the kinetic term of a quantum dimer model on the square lattice whichrotates two parallel dimers (in a spin-singlet configuration) by 90 degreesnaturally emerges. We also introduce an additional term in the Hamiltonian, ageneralized dimer plaquette interaction, in order to realize a closer analogyto the latter model. For a strong dimer plaquette attraction stabilizing acolumnar phase, a spontaneous dimerization takes place in the direction of thecolumns of (spin-carrying) dimers. Using exact diagonalizations oftwo-dimensional periodic clusters, the analysis of the low-energy spectrum andof several types of correlation functions gives indeed evidence for a new typeof lattice symmetry breaking phase, the eight-fold degenerate MixedColumnar-Plaquette Crystal, and for a transition from this phase to aResonating-Singlet-Pair Crystal (found in previous studies) which restores therotational symmetry of the lattice. Similar conclusions and phase diagram arealso reached from a simple variational approach.

Mixed Columnar-Plaquette Crystal of correlated fermions on the 2D pyrochlore lattice at fractional filling