This is a previously asked question reposted here to make searching our new forum more useful. ITensor user ajit_kumar_sorout asked:
I am using dmrg in the ITensor Julia version to calculate various excited states in the 1D spin system. There is a Z2 spontaneous symmetry breaking which should lead to two ground states. I was wondering whether dmrg output for ground state energy in ITensor provides both of these ground states ( one as ground state and the second ground state as an excited state) or a linear combination of them leads to ground state. I would like to know if there is any way to get both ground states rather than a linear combination.
Also, while calculating excited state energy using dmrg, how does the choice of “Weight” will impact the answer? What would be a good guess ( or approach) for choosing the value of “Weight” if a gap is closing between the excited state and ground state or the gap is very small?
A short answer is that the true ground state of a symmetric system which breaks a symmetry is a symmetric linear combination of the symmetry-broken (quasi-) ground states. But this true ground state is only lower in energy by a very tiny amount than the symmetry-broken states, and has higher entanglement in general. So in practice on moderate to large system sizes DMRG will return a symmetry broken state. It can be a helpful technique to actually force this to happen by applying “pinning” fields on the edge sites to go ahead and select one of the symmetry breaking scenarios.
Regarding the Weight parameter, I don’t know a clear theory about how it should be chosen, but I believe it should be larger than the gap between the ground and first excited states. (Otherwise the energy penalty, which the weight adjusts, may not be strong enough for the returned state to be orthogonal.) So I’d recommend proceeding by guessing a moderately large value for the weight, then checking afterward that the returned state is really orthogonal to the previous ones. If you have any problem with convergence, try lowering the weight.
Test this all out on small system sizes, and it’s always a good idea to plot real-space properties of your states, especially for excited states which often need many more sweeps to converge fully.