Another non-phase change method is the reverse Brayton cycle. Kind of like running a gas turbine in reverse. I think it is somewhat widely used in cryocooling,

Another non-phase change method is the reverse Brayton cycle. Kind of like running a gas turbine in reverse. I think it is somewhat widely used in cryocooling, and in jet airliner cabin AC, but it seems to not have caught on for domestic heat pump applications. Presumably the traditional phase change approaches are more efficient in the relevant temperature ranges.