Hi! I'm working on a spin system, whose Hamiltonian for particular set of parameters should result in a ferromagnetic ground state, and for different set of parameters with an antiferromagnetic one. At the beginning I was initializing the system in an antiferromagnetic state and running finite DMRG to obtain the ground state and a few excited ones. For small systems I got results agreeing with the theory. Also, what's important, the ground state was degenerated (spins were pointing once in one direction of some axis, and the other time in the opposite direction).
But while I increase the size of the system, I don't get a "homogeneous" ground state. In fact, I have alternating areas with spin pointing once in one direction and second time in the other. So, I changed the initial state of the system from the antiferromagnetic state to a ferromagnetic one, and got desired ferromagnetic ground state. But I didn't get the second ground state with spin pointing in the other direction (I believe, that's because DMRG could not find the second global minimum, while already being in one).
So my question is - how to deal with this problem? Should I run my calculations three times for a given set of parameters in Hamiltonian with changing initial state (two cases of a ferromagnetic state and the antiferromagnetic one) and compare obtained results?