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Holographic quantum phase transitions and interacting bulk scalars

We consider a system of two massive, mutually interacting probe real scalar fields, in zero temperature holographic backgrounds. The system does not have any continuous symmetry. For a suitable range of the interaction parameters adhering to the interaction potential between the bulk scalars, we have shown that as one turns on the source for one scalar field, the system may go through a second order quantum critical phase transition across which the second scalar field forms a condensate. We have looked at the resulting phase diagram and numerically computed the condensate. We have also investigated our system in two different backgrounds: $AdS_4$ and $AdS$ soliton, and got similar phase structure.