Marty is correct. There is no pressure barrier between the cockpit and cabin of a pressurized airliner. For that matter, there is also no pressure barrier between the cargo hold and passenger cabin, another common misnomer. Bleed air is used to maintain the pressure differential, and air is not recirculated, it goes out the outflow valve, which maintains the pressure differential or cabin altitude, depending on how the pressurization system is set up.