Frustrated electrons on a spatially anisotropic triangular lattice: Emergent competition of charge orders and exotic disorders due to thermal fluctuations

Abstract

We study the interplay of correlation and thermal fluctuation in a system consisting of two species of classical particles with up and down spin on a geometrically frustrated anisotropic triangular lattice, described by an extended four-state Potts model. The model corresponds to the strong coupling limit of the extended Hubbard model at quarter-filling, which is known to host several competing charge ordered phases as well as an exotic quantum state called pinball liquid. The frustrated intersite Coulomb interactions together with the on-site Coulomb interaction generate macroscopically degenerate manifolds of low-energy states. They compete entropically at finite temperature and two characteristic states emerge; a threefold periodic charge ordered state and a quasi-one-dimensionally disordered state called ``good defect state'' characterized by the systematic generation of ferroelectric bonds. The two states show good correspondence with the threefold charge order and the pinball liquid in the extended Hubbard model, and are separated by the partial Mott transition taking place on one of the three sublattices of the triangular lattice.