The schematic is almost correct. On the left, the AC source should be coupled to detector diode by another capacitor to make sure the DC circuit is not affected by AC source impedance.
If you noticed, the DC source has 0.7 V DC voltage which "opens" the detector diode into an optimum operating point, with the best detection features. This is called "DC biased" detector, and can respond well to weaker AC input signal compared to the same detector without DC bias.
Time constant on the detector R-C output determines detector response- a small time constant makes the detector response "peak" while a longer constant can be adjusted for a good response to modulated RF signals.
You can achieve an improvement if you replace the first R on the left with another diode, then you must set the DC bias to ~1.3...1.4 V as it opens both diodes.
Following the detector circuit, you can use either an opamp or any kind of audio amplifier to listen to AM signals.