The interplay between strong electronic correlations and the inherent frustration of certain lattice geometries is a common mechanism for the formation of nontrivial states of matter. In this work, we theoretically explore the collective electronic effects in the monolayer ${\mathrm{Nb}}_3{\mathrm{Cl}}_8$, a recently discovered triangular lattice Mott insulator. Our advanced many-body numerical simulations predict the emergence of a phase separation region upon doping this material. Notably, in close proximity to the phase separation, the static charge susceptibility undergoes a drastic change and reveals a distinctive bow-tie structure in momentum space. The appearance of such a fingerprint in the context of spin degrees of freedom would indicate the formation of a spin ice state. This finding allows us to associate the observed phase separation to a charge ice state, a state with a remarkable power law dependence of both the effective exchange interaction and correlations between electronic densities in real space.

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• Charge order
• Phase separation
• Phase transitions
• Quasiparticles & collective excitations
• Diagrammatic methods
• Dynamical mean field theory
• Many-body techniques