Anisotropic Lattice Strips and Magnetic Polarons

Let us consider triangular lattice strips formed by L two-site weakly 

Hamiltonian has a form of a sum of Hamiltonians that describe the interaction of neighboring segments  

Making use of the consideration proposed by Klein and Seitz [39] for the atomic limit of the linear Hubbard chain one performs averaging over the ground state of Hi and obtains the following effective Hamiltonian that describes low-lying states of (27)  

It is easily seen that (28) has a form of uniform one-dimensional Heisenberg spin Hamiltonian with a well-known spectrum. Therefore the ground state spin of our lattice has a minimal value at p 1 and a maximal value at p 1. 

Total lattice Hamiltonian is the sum of the Hamiltonians describing the interaction of neighbor segments. Therefore in the second PT order in t2 for positive values of z, the lattice with one electron per segment has a degenerate energy spectrum (because of hole-particle symmetry, positive values of t correspond to the model with more than one electron per site). This degeneracy 

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