Anderson's Orthogonality Catastrophe for One-dimensional Systems

Abstract

We derive rigorously the leading asymptotics of the so-called Anderson integral in the thermodynamic limit for one-dimensional, non-relativistic, spin-less Fermi systems. The coefficient, $\gamma$, of the leading term is computed in terms of the S-matrix. This implies a lower and an upper bound on the exponent in Anderson's orthogonality catastrophe, $\tilde{C}{N}^{-\tilde{\gamma }}\le {\mathcal{D}}_N\le C{N}^{-\gamma }$ pertaining to the overlap, ${\mathcal{D}}_N$, of ground states of non-interacting fermions.

39 pages

References in corpus (1)

• Energy Cost to Make a Hole in the Fermi Sea

Cited by in corpus (6)

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• Ground-state energy of one-dimensional free Fermi gases in the thermodynamic limit
• On an integral formula for Fredholm determinants related to pairs of spectral projections