TeNPy Forum

Hi,
In the case of the Bose-Hubbard chain, while I calculated charged energy gap (\(\Delta_c=E_0(N+1)+E_0(N-1)-2E_0(N)\)) for L=even, I found the density waves regime as gapped. However, if we do the same calculation with L=odd ( the same even length+1), I found the energy gap as 0, sometimes negative. Although I am not sure but is this problem related to the way it is programmed? As the truncation error is good enough and it converges (norm_error), I don't think it is related to bond-dimensions.

Short answer: Honestly, I don't know.
From my limited experience with Bose-Hubbard physics, I could certainly imagine this to be a physical effect.
Some suggestions for further investigation:

• Double-check that you're converged in the Nmax parameter of the BosonSite, i.e. how many bosons can occupy a site at once.
• Did you calculate \(E_0(N+2), E_0(N-2)\) as well and check for consistency? In general, the charge gap is a function of N.
  Does the effect appear with N being even/odd, or L? (I assume you chose N=L? Or what filling are you working at?)
• Did you try digging into the literature? I'd assume people have calculated the charge gap before...
• You could also try to check whether the effect appears on a small system with ED.

Thank you for the suggestions. After I checked with ED and N being odd/even, I realized it is a physical effect. Now, I can interpret why it should be gapless or gapped depending on N. Most literature followed even L=N for the energy gap calculations in DMRG, so I wanted to make sure if it is related to numerics or physics. Again, thanks for all the nice suggestions.