Main Question or Discussion Point
please refer me a good book for the detail step by step study on the second quantization. and also where can I find the jellium model for the metal?
I have studied quantum mechanics but not the quantum field theory.It depends a little on your background. Flensburg and Bruus' book is a pretty gentle introduction and written in a fairly modern way. I quite like Fetter and Walecka, which is a bit more advanced but also more detailed (it is also a little bit older, but I don't think it suffers due to its age).
The "classic" is Abrikosov, Gor'kov, and Dzyaloshinkii, but it is famously very Russian (extremely concise, dense, and equation-heavy).