What we really want is an ideal diode with zero voltage drop. Sadly, such a thing does not exist; however, there is a type of diode with a lower voltage drop — the Schottky diode. What we really want ...

And here it is, modelled using LTSpice. It is the same circuit as the classic simple precision rectifier (set to pass the negative half-sine), but with the non-inverting input of the op-amp connected ...