Effect of Finite Impurity Mass on the Anderson Orthogonality Catastrophe in One Dimension

Abstract

A one-dimensional tight-binding Hamiltonian describes the evolution of a single impurity interacting locally with $N$ electrons. The impurity spectral function has a power-law singularity $A(ω)\propto\midω-ω_0\mid^{-1+β}$ with the same exponent $β$ that characterizes the logarithmic decay of the quasiparticle weight $Z$ with the number of electrons $N$, $Z\propto N^{-β}$. The exponent $β$ is computed by (1) perturbation theory in the interaction strength and (2) numerical evaluations with exact results for small systems and variational results for larger systems. A nonanalytical behavior of $β$ is observed in the limit of infinite impurity mass. For large interaction strength, the exponent depends strongly on the mass of the impurity in contrast to the perturbative result.