The observation of charge stripe order in the doped nickelate and cuprate materials has motivated much theoretical effort to understand the underlying mechanism of the stripe phase. Numerical studies of the Hubbard model show two possibilities: (i) stripe order arises from a tendency toward phase separation and its competition with the long-range Coulomb interaction or (ii) stripe order inherently arises as a compromise between itinerancy and magnetic interactions. Here we determine the restricted phase diagram of the two-dimensional Falicov-Kimball model and see that it displays rich behavior illustrating both possibilities in different regions.
The spinless Falicov-Kimball model on a two-dimensional square lattice is studied using the method of restricted phase diagrams constructed in the grand canonical ensemble. The results are compared with the one-dimensional model. Although the two-dimensional phase diagrams are more complex, with several distinct families of ion configurations occurring as ground states, there are surprising similarities with the one dimensional case. Within each family of configurations, the ground states form a devil's staircase structure and the configurations are constructed according to a composition rule identical to that in one dimension. It is also found that, as in one dimension, segregation occurs in the non-neutral model for large ion-electron interaction strength. Some features of the phase diagrams are understood by examining the effective two body ion interaction.
The exact solution for the thermodynamic and dynamic properties of the infinite-dimensional multi-component Falicov-Kimball model for arbitrary concentration of d-and f-electrons is presented. The emphasis is on a descriptive derivation of important physical quantities by the equation of motion technique. We provide a thorough discussion of the f-electron Green function and of the susceptibility to spontaneous hybridization. The solutions are used to illustrate different physical systems ranging from the high-temperature phase of the YbInCu 4 family of materials to an examination of classical intermediate valence systems that can develop a spontaneous hybridization at T = 0.
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