You are missing that any heat engine (including photovoltaics !) is limited by the Carnot efficiency. And a heat pump is just a reverse heat engine. And you are

You are missing that any heat engine (including photovoltaics !) is limited by the Carnot efficiency. And a heat pump is just a reverse heat engine. And you are trying to couple their inputs and outputs in a loop. I'm not sure that this would even qualify as a perpetual motion machine of the second kind ? P.S.: A heat pump is usually able to "cheat" an "efficiency" (aka Coefficient of Performance) over 100% because (for a refrigerator) it's defined as the inverse of the usual Carnot efficiency. When you want heating, you artificially get up to +100% to the CoP from the spent "mechanical" power being 100% converted into heat. EDIT : Ugh, took a while to get this right !