I have a short question. In the following line, "left" means that the hamiltonian used to define the initial density operator was built by left product between operators? Am I right? Or what is the meaning of "left"?
parameters.rho0=equilibrium(spin_system,hamiltonian(assume(spin_system,'labframe'),'left'));
"left" specification for rho_0
Re: "left" specification for rho_0
That requests a left side product superoperator. That is because the equilibrium state is computed in Liouville space as exp(-H_left/kT)*unit_vector, and the commutation superoperator (default) would not be correct here. You can see this directly from the Taylor expansion of that definition, it's basically a column stretch of exp(-H/kT).