Okay, let me try hard to pose this question as clear as I can.
Let's take a quantum system where a single charge carrier interacts with a bosonic mode. Examples would be the Holstein model where a tight-binding carrier interacts with dispersionless phonons, or maybe a single carrier in a magnetic lattice where it can excite magnons.
The typical single particle spectral function then has a bunch of generic features: There might be a bound state, appearing as a sharp peak in the spectrum, and there'll also be a continuum of states that are associated with the "free" particle plus a bosonic excitation. For example, in the Holstein model there'll be a sharp peak for the Holstein polaron, at some energy $E_0$, and then a continuum of "polaron + a free phonon" states starting at energy $E_0 + \Omega$ where $\Omega$ is the energy of the bosonic mode (with $\hbar = 1$).
So far, so good, I've worked with the Holstein model and some more complicated variatons of it for quite some time. Now I'm looking at something more complicated, and I'm looking at it in the two-particle sector, and here's a simple question:
When I see a continuum in the spectrum, should there always be a simple interpretation for that continuum? As in, I look at where the continuum starts and then I can tell immediately: "Ah yes, this is the continuum of two independent single-carrier bound objects" or "Yes, this is the continuum of ground-state-plus-one-bosonic-excitation states"? Or could there be continua that are more complicated in nature and aren't amenable to a straightforward interpretation?
I'm asking because I'm trying to decide whether something my simulation spits out is a bug or a feature... I see a continuum of states well below where the "two independent single-particle-bound-states" continuum would lie, but below this continuum I'd only expect a bound state...