Exact Many-Electron Ground States on the Diamond Hubbard Chain

Exact ground states of interacting electrons on the diamond Hubbard chain in a magnetic field are constructed which exhibit a wide range of properties such as flat-band ferromagnetism and correlation-induced metallic, half-metallic, or insulating behavior. The properties of these ground states can be tuned by changing the magnetic flux, local potentials, or electron density.

Figure 1

Diamond Hubbard chain. The cross-shaped region depicts a localized (Wannier) eigenfunction for $t_{\perp }=t_{\parallel }=0$ and flux $\delta =\pi /2$ (see text).

Figure 2

Single-electron band structure. (a) $t_{\perp }=t_{\parallel }=0$, $\delta =\pi /2$. (b) $ϵ=-t_{\perp }+t_{\perp }^{-1}/2$, $\delta =\pi$; the upper flat bands are degenerate for $t_{\perp }{t}_{\parallel }=1/4$. (c) $t_{\parallel }=0$, $ϵt_{\perp }\cos \delta =t_{\perp }^2-{cos}^2\delta$.