Hello,
I am working with a Hamiltonian with ZZ conservation symmetry. From what I know, if a symmetry is known for a given Hamiltonian and we can find a basis for that symmetry, then we can, instead of diagonalizing the entire Hamiltonian, look for a particular symmetry sector and basically reduce the problem size. This can help deal with larger system sizes. For Hamiltonians with spin-conservation symmetry, finding this basis is easy, we just have to look for number of up-spins or down-spins in case of spin lattices and we are done.
But in cases where we know that there is a domain-wall conservation symmetry (ZZ), finding such a good basis is not something that seems trivial.
If anyone has read papers on this or has research regarding this, I would be glad to discuss.
P.S: Pardon my misuse of simple terms, just wanted to make the post accessible
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