Metal-insulator transition caused by the coupling to localized charge-frustrated systems under ice-rule local constraint

We report the results of our theoretical and numerical study on electronic and transport properties of fermion systems with charge frustration. We consider an extended Falicov-Kimball model in which itinerant spinless fermions interact repulsively by U with localized particles whose distribution satisfies a local constraint under geometrical frustration, the so-called ice rule. We numerically calculate the density of states, optical conductivity, and inverse participation ratio for the models on the pyrochlore, checkerboard, and kagome lattices, and discuss the nature of metal-insulator transitions at commensurate fillings. As a result, we show that the ice-rule local constraint leads to several universal features in the electronic structure; a charge gap opens at a considerably small U compared to the bandwidth, and the energy spectrum approaches a characteristic form in the large U limit, that is, the noninteracting tight-binding form in one dimension or the $\delta$-functional peak. In the large U region, the itinerant fermions are confined in the macroscopically-degenerate ice-rule configurations, which consist of a bunch of one-dimensional loops: We call this insulating state the charge ice. On the other hand, transport properties are much affected by the geometry and dimensionality of lattices; e.g., the pyrochlore lattice model exhibits a transition from a metallic to the charge-ice insulating state by increasing U, while the checkerboard lattice model appears to show Anderson localization before opening a gap. Meanwhile, in the kagome lattice case, we do not obtain clear evidence of Anderson localization. Our results elucidate the universality and diversity of phase transitions to the charge-ice insulator in fully frustrated lattices.Comment: 16 pages, 17 figure

Quantum melting of charge ice and non-Fermi-liquid behavior: An exact solution for the extended Falicov-Kimball model in the ice-rule limit

An exact solution is obtained for a model of itinerant electrons coupled to ice-rule variables on the tetrahedron Husimi cactus, an analogue of the Bethe lattice of corner-sharing tetrahedra. It reveals a quantum critical point with the emergence of non-Fermi-liquid behavior in melting of the "charge ice" insulator. The electronic structure is compared with the numerical results for the pyrochlore-lattice model to elucidate the physics of electron systems interacting with the tetrahedron ice rule.Comment: 5 pages, 4 figure