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Motivated by recent progress in preparing alkali-metal compounds, we present the magnetic and
electronic phase diagram of the quasi-one-dimensional alkali metal iron selenide Na₂FeSe₂ . The
novelty of this material is that it has both a dominant chain geometry in the structure and the valence of iron is Fe²⁺.
We derive a realistic three-orbital tight-binding model based on ab initio calculations. We have constructed the ground-state phase diagram for Na₂FeSe₂, using density-matrix-renormalization group and Lanczos methods. We find a robust region of block state, with two-spin ferromagnetic clusters coupled antiferromagnetically. The phase diagram also contains a large region of staggered spin order at large Hubbard repulsion. In addition to these phases, near the block-to-staggered transition region, an exotic phase is stabilized with a mixture of both states: an inhomogeneous orbital-selective charge density wave with the exotic spin configuration. Our predictions for Na₂FeSe₂, should be of interest to both theorists and experimentalists working on the realization of block states in one-dimensional iron selenide chain materials.