There are isolated pockets of Monomorium pharaonsis and Paratrechina longicornis, but this wouldn't necessarily constitute "invasive".
Sadly, this description does not tell us much. The only local ants which are small enough to be ~1mm are
Cardiocondyla obscurior, Strumigenys, Brachymyrmex depilis, and the Solenopsis thief ants -- all of which are pale or brown. At slightly larger, Hypoponera opacior might be a candidate. You're sure it's 1mm, right?