Abstract
In this work, we study the extended Falicov–Kimball model at half-filling within the Hartree–Fock approach (HFA) (for various crystal lattices) and compare the results obtained with the rigorous ones derived within the dynamical mean field theory (DMFT). The model describes a system, where electrons with spin-↓ are itinerant (with hopping amplitude t), whereas those with spin-↑ are localized. The particles interact via on-site U and intersite V density–density Coulomb interactions. We show that the HFA description of the ground state properties of the model is equivalent to the exact DMFT solution and provides a qualitatively correct picture also for a range of small temperatures. It does capture the discontinuous transition between ordered phases at U = 2V for small temperatures as well as correct features of the continuous order–disorder transition. However, the HFA predicts that the discontinuous boundary ends at the isolated-critical point (of the liquid-gas type) and it does not merge with the continuous boundary. This approach cannot also describe properly a change of order of the continuous transition for large V as well as various metal–insulator transitions found within the DMFT.
Highlights
Interparticle correlations in fermionic systems give rise variety of intriguing phenomena
We can further restrict ourselves to find the solutions of (4)–(5) only with ∆↑ ≥ 0
These properties are connected with an equivalence of both sublattices of an alternate lattice
Summary
Interparticle correlations in fermionic systems give rise variety of intriguing phenomena. Description of correlated electron systems requires special care and precision, because sometimes it happens that different calculation methods lead to qualitatively different results, e.g., the dependence of order-disorder transition temperature as a function of Hubbard-U interaction in the attractive Hubbard model (i.e., superconducting critical temperature) [1, 24,25,26,27] as well as in the spin-less Falicov-Kimball model (vanishing of charge order) [28, 29].
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