{\it Ab initio} Evidence of Strong Correlation Associated with Mott Proximity in Iron-Based Superconductor

Recently discovered iron-based superconductors have attracted much interest because of their high superconducting critical temperatures ($T_{c}$). Although it is believed that electron correlations play key roles in the unconventional high-$T_{c}$ superconductivity, their roles are not fully understood yet. To clarify electron correlation effects from a microscopic point of view, we study the {\it ab initio} low-energy effective models for iron-based superconductors by using multi-variable variational Monte Carlo (mVMC) method. From the {\it ab initio} calculations, we show that the iron-based superconductors found around $d^6$ configuration (namely, five Fe 3$d$ orbitals filled by 6 electrons on average) are under the umbrella of an unexpectedly large-scale dome of correlated-electron matter centered at the Mott insulator at $d^5$ (namely, half filling). This proximity of the large-dome of strong electron correlations yields a variety with bad insulating (or incoherent metallic) states, quantum criticality of antiferromagnetism, orbital fluctuations and differentiations arising from interplay between the Hund's rule coupling and Mott physics.