Can Singlets Be Shared in Valence Bond Solid States?

[mavipranav]

Hello

I have come across this inexplicable fact mentioned in somewhere that for a chain of S = 1 spins, the adjacent bonds can all be in a singlet state i.e. singlets can be shared in this case (forming valence bond solids) but not, for example, for |S| = 1/2, the latter point being clear. I do not understand how singlets can be shared. Can someone mention what the shared-wavefunction across 3 sites looks like?

Thanks,
Mavi

 

[mavipranav]

The answer comes from the AKLT hamiltonian, wherein at each site, the spin 1 is decomposed into 2 spin-1'2's. This is the ground state of the said hamiltonian and can be best understood within the Schwinger boson formalism.