How to deal with varying final results for different initial states of the system, while doing DMRG calculations?

Question

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?

Answer 1

Thanks for the question. Yes, trying multiple initial states, especially when you suspect a convergence issue, is an important technique in DMRG.

There are some other techniques and considerations you can use also:

1. try setting the "noise" DMRG sweeping parameter to be non-zero during some or all of your sweeps. It can often help with convergence.

2. modify your Hamiltonian on the boundary of your system to lift ground state degeneracies by adding "pinning fields". For example, in the case of a ferromagnetic phase, adding a uniform magnetic field to the boundary sites of your system will cause the true ground state to be the one aligned with the field.

3. of course, make sure you are doing sufficiently many sweeps to really converge your result (I assume you are already doing this one)

Best regards,
Miles