AN EXACTLY SOLUBLE ONE-DIMENSIONAL QUANTUM-MECHANICAL HEISENBERG AND NAGAOKA T-J MODEL

For a quasi-one dimensional sawtooth topology the authors show that the quantum mechanical ground state of the Heisenberg Hamiltonian has only nearest neighbour singlet correlations. The ground state is multiply degenerate with precisely as many ground states as atoms in the system. In fact they can associate each ground state with a special site that has a fixed spin. Allowing this special site to become a hole, in a frustrated t-J description, allows them to deduce the ground state for the motion of one hole in the presence of the Heisenberg interactions. When the hopping is unfrustrated they look at the competition between t and J and find a reasonable description for a 'polaron'. The polaron maintains low spin.