How to systematically find the symmetry operator given a Hamiltonian?

[quantumbitting]

For instance,how to systematically derive the equns 2.2 & 2.5 given a Hamiltonian on the article below?;
arxiv.org/pdf/0904.2771.pdf .

 

[azntoon]

Unfortunately, it is not possible to answer this question without more specific information on the Hamiltonian being referred to. In order to derive equations 2.2 and 2.5, you need to know what terms are present in the Hamiltonian and how they interact with each other. Without this information, it is impossible to derive the equations.