The Company I worked for did extensive studies of just such shallow depth heat pump systems for central heating of homes, to the point that they decided to sell off their Central Heating boiler business (rather prematurely as it turned out) to concentrate on Sanitary Ware
Such is life.
I believe heat pumps are not actually geo thermic. Daughter has a air sourced heat pump system, which basically takes energy from cool air and kicks it out cooler. Ground heat pumps work in same way,they need a fair amount of power to operate but will provide upto 3 to 5 times the amount consumed in heat output. (think using fridge pipes at back of fridge to heat stuff)
Years and years ago a similar system used Thames to heat Albert hall. (not sure of actual temps but basically water from Thames came in at let say 13 degrees, left at 6 degrees and the energy left behind used to heat the building, ie a water sourced heat pump. Mitsubishi are leaders in air sourced heat pumps(seen quite a few but no other makers) . A friend in France has same system but ground sourced.(You need a big garden) He heats pool and runs central heating. System consumes at peak( I believe) 5kwh but provides 20kwh.
I dont think such systems can produce electricity (I have never seen one anyway) They are limited to heating. (or cooling when required)
I think they are refered to as ground sourced heat pumps. I believe geothermic refers to actual heat produced in volcanic active areas. (could be wrong tho)
Daughters system works down to minus 5 C at which temp it still doubles energy consumed. (ie consumes 5kwh but provides 10kwh heating. At 15 degrees C it operates at x5 but who needs heating when temp is 15...
Below - 5 the system becomes purely electrical,at which point ground sourced would still be operating.