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

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

1996-09-25

arxiv.org/abs/cond-mat/9609247v1

Phys. Rev. B 54 (1996) 17422.

Physics

Condensed Matter

26 pages, RevTeX, 7 figures included, to be published in Phys. Rev. B

Scientific paper

10.1103/PhysRevB.54.17422

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.

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