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Pairing in a tight-binding model with occupation-dependent hopping
rate: exact diagonalization study

H.Q. Lin and J.E. Hirsch, Phys. Rev. B
**52**, 16155 (1995).

The Hubbard model with occupation-dependent hopping rate
exhibits superconductivity
in a wide range of parameters within mean field (BCS) theory. Here we study
pair binding energies in this model for small clusters by exact
diagonalization of the Hamiltonian. The model is defined by on-site and
nearest neighbor repulsions $U$ and $V$, and occupation-dependent
hopping rate $t(n)=t+n\Delta t$. We present results for one-dimensional chains
and for two-dimensional square lattices of sizes $4\times 4$, $6\times 6$ and
$8 \times 8$. As a function of carrier density $n$
the pair binding energy first increases and then decreases, and vanishes
beyond a critical density. BCS results for the pair binding energy are found
to be in remarkably good agreement with the exact results.
In particular, BCS theory accurately reproduces the range of
interaction parameters where pair binding exists in the exact solution.
The model is found to exhibit no tendency to phase separation or
clustering of more than two particles even for parameters giving
rise to strong pair binding, in contrast to other tight binding
models where pairing occurs.

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