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Anomalous orthogonality catastrophe for Luttinger liquid with repulsion

Alexander O. Gogolin

Published Jan 1, 1993• 0 citations
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Physical Review Letters•Nov 1, 1993•78 citations
The behavior of a single impurity in a one-dimensional Luttinger liquid is numerically investigated by means of the density-matrix renormalization group. By analyzing the finite-size scaling behavior of the low-energy spectrum, we confirm the theoretical prediction of Kane and Fisher [Phys. Rev. Lett. 68, 1220 (1992)] both for attractive and repulsive interactions. Moreover, we calculate the exponent of the orthogonality catastrophe, which gives a further support to the above theoretical prediction.
The response of the Luttinger liquid to a local potential is studied at zero temperature. It exhibits a crossover behavior. On the largest time scale and in the case of repulsive electron-electron interaction, the backscattering from the potential contributes to the core-hole Green's function G(t) the factor (t0{\mathit{t}}_{0}t0​/t)1/8{)}^{1/8})1/8---a universal (potential independent) decay law. The orthogonality catastrophe remains of the same analytical type as for the simple metals.