two arduino's I2C - power option

Hello all,

I’ve been using two arduino’s uno connected via I2C (A4,A5) and ground of both connected. They are powered separately each one from two AA batteries via a step-up to 5v. It is working 100% and the master arduino is sending the data correctly to the slave.

However I’d like to have only one pack of 2xAA powering both of them. In this case I assume I must remove the ground wire connecting them to avoid a ground loop. Is that correct?

Thank you

Any input please?

Thank you