I want to study about order parameter and symmetry breaking related to bose einstein condensation in interacted system. Which book i should read? also i want to learn this in second quantization notation.
1 Answer
I mean the two main textbooks for this are:
Pethic & Smith, Bose Einstein condensation in dilute gases
Stringary & Pitaevski, Bose Einstein condensation (and Superfluidity)
which cover both the theory and the experimental stuff.
Otherwise, any lecture notes online cover the basics of BEC.
As a quick answer to the key words in your title/question:
The order parameter is usually chosen as the population in the ground state $|\Psi_0|^2$ which is $\sim 0$ for $T>T_c$ and $\underbrace{\neq}_{\text{macroscopically}} 0$ for $T<T_c$ and $1$ at $T=0$.
The symmetry broken is $U(1)$, since the BEC is a single mega-wavefunction with just one phase. The choice of a single phase breaks the $U(1)$ (the group of phase factors) symmetry of the thermal state.