Spin polarons and the Hubbard bands

As U/I (or U/B) goes to infinity, then so does R/a. Moreover, the energy of the spin polaron at rest tends to —%B. It follows that the bandwidth is B and, in the limit when U/B is large, is unaffected by the Hubbard U. 

Our estimate of the band form should therefore show strong peaks at the extremities due to the (heavy) spin polarons. For these, k is a good quantum number, as long as kR 1. If this is not so, the polaron concept breaks down and we come into the region investigated by Brinkman and Rice (1970a) where the electron loses energy rapidly to spin excitations and k is a band quantum number. These authors estimate that the bandwidth contracts by about 70%. 

We are interested in the situation near the metal-insulator transition when U 2zl, and for this case, from (10), 

Our conclusion is, then, that near the transition the spin polaron spreads only to the nearest and perhaps next-nearest neighbours. 

Such spin polarons should not have a mass much greater than m in Si P. Moreover, they can pass freely from one atom to another, and are not impeded by the antiferromagnetic order. Thus the bandwidth of each Hubbard band should, we believe, still be of order 2zl, as it is for large values of U/B, and the equation 

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