I would like to investigate bosons in a 1D harmonic trap, and was hoping that this could be done by using DMRG in the continuum limit of having many more sites than particles.

As a test case, I have simulated one boson in a trap with the Hamiltonian

However, the density, as measured with

does not converge towards the harmonic oscillator ground state for up to 100 sweeps on 1000 sites with small lattice constant in a system large enough that the particle does not feel the walls of the box. All other DMRG parameters were also generously set. It seems that for t >> \omega, the system tends towards the particle in a box ground state (which converges nicely if there is no trap), and for t <= \omega, the system tends towards a much more localized ground state than the harmonic oscillator ground state, see the figure which has \omega = 2t. Note that the DMRG potential is the potential felt at every point as output by the DMRG code.

I am aware that iTensor DMRG is not designed for the continuum limit, but it has been used to investigate that limit in several published papers. I cannot find any DMRG parameters whose adjustment changes any of this, apart from those energies. Can you help me figure out what is going on?