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The local Tomonaga - Luttinger liquid in the one-dimensional Hubbard model with a boundary field

The properties of the one-dimensional Hubbard model with a boundary field are studied. In the strong-coupling limit, the compressibility and the susceptibility induced by the boundary field are evaluated using the Bethe ansatz equation. These quantities are governed by the density of states at the Fermi level. The results obtained from our calculations seem to suggest that the local state induced by the boundary field realizes the local Tomonaga - Luttinger liquid.