Interacting spinless fermions in a diamond chain

Abstract

We study spinless fermions in a flux threaded AB${}_2$ chain taking into account nearest-neighbor Coulomb interactions. The exact diagonalization of the spinless AB${}_2$ chain is presented in the limiting cases of infinite or zero nearest-neighbor Coulomb repulsion for any filling. Without interactions, the AB${}_2$ chain has a flat band even in the presence of magnetic flux. We show that the respective localized states can be written in the most compact form as standing waves in one or two consecutive plaquettes. We show that this result is easily generalized to other frustrated lattices such as the Lieb lattice. A restricted Hartree-Fock study of the $V/t$ versus filling phase diagram of the AB${}_2$ chain has also been carried out. The validity of the mean-field approach is discussed taking into account the exact results in the case of infinite repulsion. The ground-state energy as a function of filling and interaction $V$ is determined using the mean-field approach and exactly for infinite or zero $V$. In the strong-coupling limit, two kinds of localized states occur: one-particle localized states due to geometry and two-particle localized states due to interaction and geometry. These localized fermions create open boundary regions for itinerant carriers. At filling $\rho =2/9$ and in order to avoid the existence of itinerant fermions with positive kinetic energy, phase separation occurs between a high-density phase ($\rho =2/3$) and a low-density phase ($\rho =2/9$) leading to a metal-insulator transition. The ground-state energy reflects such phase separation by becoming linear on filling above 2/9. We argue that for filling near or larger than 2/9, the spectrum of the t-V AB${}_2$ chain can be viewed as a mix of the spectra of Luttinger liquids (LL) with different fillings, boundary conditions, and LL velocities.

17 pages, 17 figures

References in corpus (9)

• Flat bands and Wigner crystallization in the honeycomb optical lattice
• The $p_{x,y}$-orbital counterpart of graphene: cold atoms in the honeycomb optical lattice
• Nature of the spin dynamics and 1/3 magnetization plateau in azurite
• Exact eigenstates and macroscopic magnetization jumps in strongly frustrated spin lattices
• Low-temperature properties of the Hubbard model on highly frustrated one-dimensional lattices
• Exact many-electron ground states on the diamond Hubbard chain
• Exact Insulating and Conducting Ground States of a Periodic Anderson Model in Three Dimensions
• Doped AB_2 Hubbard Chain: Spiral, Nagaoka and RVB States, Phase Separation and Luttinger Liquid Behavior
• Structural instability of two- and three-dimensional pyrochlore spin lattices in high magnetic fields

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