  The magnetic and electronic phase diagram of a model for the
quasi-one-dimensional alkali metal iron selenide compound Na$_2$FeSe$_2$ is
presented. The novelty of this material is that the valence of iron is
Fe$^{2+}$ contrary to most other iron-chain compounds with valence Fe$^{3+}$.
Using first-principles techniques, we developed a three-orbital tight-binding
model that reproduces the {\it ab initio} band structure near the Fermi level.
Including Hubbard and Hund couplings and studying the model via the density
matrix renormalization group and Lanczos methods, we constructed the ground
state phase diagram. A robust region where the block state $\uparrow \uparrow
\downarrow \downarrow \uparrow \uparrow \downarrow \downarrow$ is stabilized
was unveiled. The analog state in iron ladders, employing 2$\times$2
ferromagnetic blocks, is by now well-established, but in chains a block
magnetic order has not been observed yet in real materials. The phase diagram
also contains a large region of canonical staggered spin order $\uparrow
\downarrow \uparrow \downarrow \uparrow \downarrow \uparrow$ at very large
Hubbard repulsion. At the block to staggered transition region, a novel phase
is stabilized with a mixture of both states: an inhomogeneous orbital-selective
charge density wave with the exotic spin configuration $\uparrow \uparrow
\downarrow \uparrow \downarrow \downarrow \uparrow \downarrow$. Our predictions
for Na$_2$FeSe$_2$ may guide crystal growers and neutron scattering
experimentalists towards the realization of block states in one-dimensional
iron-selenide chain materials.
