Dear forum,

I have a 1D chain where half of the sites are singly occupied while the other half are vacant and double occupancy on any site is not allowed. I modeled this system with spin-1/2 and spin-1 site sets to compare my results. For both the cases, the values of the parameters in the Hamiltonian are such that the the ground state is expected to be antiferromagnetic, which is the superposition of the two Neel states |101010...> and |010101...>.

Spin-1/2 model: The spin operators are defined such that S^z |1> = +1 |1> and S^z |0> = -1 |0> where |1> = |spin up> refers to a singly occupied site while |0> = |spin down> refers to a vacant site.

Spin-1 model: The spin operators are defined such that S^z |2> = +1 |2>, S^z |1> = 0 |1> and S^z|0> = -1 |0> where |2> = |spin up>, |1> = |spin 0> and |0> = |spin down> refer to doubly occupied, singly occupied and vacant sites respectively. There is an onsite potential U with a value large enough to avoid double occupancy on any site.

Here are the results I obtained:

For spin-1/2, ITensor gives < S^z _ j > = +-1 alternating along the 1D chain while < S^z _ j S^z_(j+1) > = -1 for all j, where j is the site index. This implies that DMRG returns only one of the Neel states as the ground state.

For spin-1, ITensor gives < S^z _ j > = -0.5 and < S^z _ j S^z_(j+1) > = -0.25 for all j. This implies that the ground state returned by DMRG is a superposition of the two Neel states |101010...> and |010101...>.

Both the spin-1/2 and spin-1 cases seem to make sense, but while the former returns only one of the two states in the superposition, the latter seems to give an average. Could you please explain why DMRG works differently for the two cases?

Thanks in advance,

Niraj