High-order coupling as a driver for Mott insulating behavior in holography

We construct a simple holographic model incorporating higher-order coupling terms for electron self-interactions. It can exhibit typical behavior of a Mott insulator, including a metal-insulator transition and a decrease in DC conductivity with the increase of charge density. In the analysis of AC conductivity, a soft gap is generally observed. Notably, when the DC conductivity approaches zero, the AC conductivity reveals a multi-peak structure, which can be attributed to the Mott and charge-transfer gaps observed experimentally in transition metals. With the increase of DC conductivity, the multi-peak structure gradually reverts to soft-gap behavior or even metallic conductivity. The accuracy of the numerical result is guaranteed by $σ(ω\to 0)=σ_{DC}$ and sum rules.