Consider a problem, where we have N spin-1 in 1D with only nearest neighbor ising coupling.

Consider N=100, and the following Hamiltonian,

$$H = \sum*{i, i \ne 50} - S^z*iS^z*{i+1} + 10 S^z*{50} S^z_{51} $$

Except the bond connecting 50th and 51st spins, all others are ferromagnetic in nature. Also note the difference in the strength of the coupling.

Clearly the ground state of this system is a state with a domain wall between the 50th and 51st sites - this has the energy 98*(-1) - 10 = -108 (in units of J=1).

However, the answer which i find depends on the initial choice. For example, when i choose the initial state to be a completely ferromagnetic state, the converged state it reaches seems to be a state with only a single spin flipped at 51st site, leading to a ground state energy of -97 - 10 + 1 = -106. Whereas in case i give a the correct state as the initial state(or close) it finds the correct ground state. For a smaller system size, (changing N), it seems more difficult to find the correct ground state.

So the question: Is the above observation an artifact of DMRG itself. Or i am missing some crucial details: like we may be able to reach the correct ground state by changing the no. of sweeps, no. of states to be kept etc. Is there an intuitive way to decide these? Next, is the question about the choice of initial state. Given, if one doesn't have much clue from the Hamiltonian, how does one know if the ground state found is indeed the correct one. And finally the question about the dependence on system size. How does these features depend on system size.

Sorry, the question seems long. Any clarification/suggestion will be most helpful. Many thanks.