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

TL;DR

This paper investigates how the finite mass of an impurity affects the Anderson orthogonality catastrophe in one-dimensional systems, revealing nonanalytical behavior and mass-dependent exponents in the spectral function.

Contribution

It introduces a combined perturbative and numerical approach to analyze the impurity spectral function and uncovers nontrivial mass effects on the orthogonality catastrophe.

Findings

Exponent  eta shows nonanalytical behavior at infinite impurity mass.

The spectral function exhibits a power-law singularity with a mass-dependent exponent.

Large interaction strength amplifies the influence of impurity mass on the spectral properties.

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 $A(\omega)\propto\mid\omega-\omega_0\mid^{-1+\beta}$ with the same exponent $\beta$ that characterizes the logarithmic decay of the quasiparticle weight $Z$ with the number of electrons $N$, $Z\propto N^{-\beta}$. The exponent $\beta$ 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 $\beta$ 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.