Orthogonality theorem for a one-dimensional-electron gas with a bounded spectrum
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The overlap between the ground-state wave functions of a one-dimensional electron gas with the Hamiltonians Ĥ0 and \(\hat H_0 \), where \(\hat H_0 + \hat V\) is the impurity potential, is calculated. It is shown that in the limit of an infinite potential the overlap vanishes as M−1/8 as M→∞, where M is the number of filled levels, while in the case of a weak potential this overlap differs little from 1. A relation is found between the magnitude of the overlap and the behavior of the density of states near the Fermi energy (statistics of the levels). The possibility of linearization of the spectrum and the possibility of performing a bosonization procedure are discussed in light of the results obtained.
PACS numbers7110.Ca 7155−i
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