persistent current in a fermionic ring

Hi Miles,
I’m beginner in DMRG. I have a question regarding the Peierls phase in a long-range interacting fermionic ring. I’m performing the DMRG calculation both with “Electron” site type and “S=1/2” site type via Jordan-Wigner mapping. The two procedures match each other but they not coincide with the non-interacting case, which can be solved almost by hand. The flux periodicity of the non-interacting case solved by hand and the one obtained by DMRG do not match. It seems to appear a size dependence which is not expected. Any help is appreciated.

Just to understand better, are you inputting a periodic Hamiltonian into DMRG or an open-boundary Hamiltonian?

Otherwise, assuming the Hamiltonian you are inputting is exactly the same as the one you are solving analytically, it’s hard to say or guess exactly where the difference is coming from. But my guess would be that it’s not the numerics per se (in the sense of DMRG giving a wrong answer) but more likely from how the Jordan-Wigner transformation interplays with the definition of flux you are using for your analytic calculation. I believe the flux translates into the phase of the hopping connecting the first to the last site of the MPS (note that the MPS is an open-boundary MPS in our code, regardless of whether the Hamiltonian has a periodic topology or not). So you might want to or need to alter the phase of the hopping term connecting site 1 to site N in order to get agreement with your analytical calculation.