First of all, thank you for your incredible work on iTensor and especially on maintaining this support page through the years! It is immensely helpful.
So, first of all I would just like to see that for N particles on M sites, taking N<<M leads to a density which is a close approximation to the continuum solution density. To converge towards the continuum energy, I would have to take into account the relationship between t and a, but it is my understanding that for just getting the right density, only the length scale of the potential really matters. Thus I am just choosing somewhat arbitrary t for now, and making sure that in each point, the value of the potential corresponds to that of the continuum potential in the same point.
But since you ask, I guess the shape of the density is an interplay between the kinetic and potential energy, and scaling them wrong might lead to the wrong density? In that case, how come I find the right particle in a box density for basically arbitrary t?
Sweeps are very cheap for N<<M, and sometimes a large number is required to converge. For a very weak trap, that is the case, but for a trap like the one pictured, not many sweeps are required. I mostly mentioned it to say that it certainly had enough sweeps to converge on a ground state.
Thank you again for taking the time to answer, and please let me know if you need anything else.