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

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

2008-06-29

arxiv.org/abs/0806.4763v2

Phys.Rev.B78, 195101 (2008)

Physics

Condensed Matter

Strongly Correlated Electrons

14 pages, 15 figures

Scientific paper

10.1103/PhysRevB.78.195101

We study a model of strongly correlated S=1/2 fermions on the planar pyrochlore, or checkerboard, lattice, at fractional (1/8) filling. Starting with the extended Hubbard model in the limit of strong Coulomb repulsion, low-energy configurations can be mapped onto hard-core dimer configurations whose dimers carry a spin degree of freedom. An effective Hamiltonian similar to the kinetic term of a quantum dimer model on the square lattice which rotates two parallel dimers (in a spin-singlet configuration) by 90 degrees naturally emerges. We also introduce an additional term in the Hamiltonian, a generalized dimer plaquette interaction, in order to realize a closer analogy to the latter model. For a strong dimer plaquette attraction stabilizing a columnar phase, a spontaneous dimerization takes place in the direction of the columns of (spin-carrying) dimers. Using exact diagonalizations of two-dimensional periodic clusters, the analysis of the low-energy spectrum and of several types of correlation functions gives indeed evidence for a new type of lattice symmetry breaking phase, the eight-fold degenerate Mixed Columnar-Plaquette Crystal, and for a transition from this phase to a Resonating-Singlet-Pair Crystal (found in previous studies) which restores the rotational symmetry of the lattice. Similar conclusions and phase diagram are also reached from a simple variational approach.

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