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I'll take it that you want this circuit to actually work, not just appear to work in some software simulation.  In that case, it's about the circuit, not the simulator.  A simulator is just one tool in designing or verifying a circuit.  A brain and a calculator are usually much better tools.

First, since your AC voltage is so low, think about using Schottky diodes.  That should give you an extra 700 mV or so of output for the same AC input.  That's about 30% more in your case.

You might not be able to use Schottky diodes if the AC source is very high impedance or very slow, or intermittent with long off-times.  In those cases the reverse leakage of Schottkys would make them worse than silicon diodes.

Your question seems to be about designing a threshold detect circuit to switch the load on and off.  How <i>"relational operatios combined with constant and logical operators"</i> work in some simulator is the wrong question.  Even if you get it working, what are you going to do?  Buy a reel of relational operatios ICs to make the actual circuit?

It would help a lot to know more about this AC signal you are harvesting power from.  What's its open-circuit voltage, impedance, availability, etc?  Probably quiescent current is an important parameter, but you haven't told us enough to know that.

You need to design a threshold-detecting circuit that takes almost no current below the threshold.  That's actually not that hard, but you have to think in terms of real parts, not what pretend-parts some simulator provides.

Once we have better parameters, we can get into a real circuit.