Correlations in one dimensional quantum impurity problems with an external field

TL;DR

This paper uses non-perturbative Bethe ansatz techniques to analyze response functions in one-dimensional quantum impurity problems with an external field, revealing exact low-frequency behaviors and singularity structures.

Contribution

It develops the first non-perturbative theory of excitations over the field-dependent ground state in quantum impurity problems, providing exact results for dynamical susceptibilities and noise.

Findings

Exact low-frequency behavior of susceptibility and noise functions

Identification of singularity structures in response functions

Differences from previous perturbative approaches

Abstract

We study response functions of integrable quantum impurity problems with an external field at $T=0$ using non perturbative techniques derived from the Bethe ansatz. We develop the first steps of the theory of excitations over the new, field dependent ground state, leading to renormalized (or ``dressed'') form-factors. We obtain exactly the low frequency behaviour of the dynamical susceptibility $\chi''(\omega)$ in the double well problem of dissipative quantum mechanics (or equivalently the anisotropic Kondo problem),and the low frequency behaviour of the AC noise $S_t(\omega)$ for tunneling between edges in fractional quantum Hall devices. We also obtain exactly the structure of singularities in $\chi''(\omega)$ and $S_t(\omega)$. Our results differ significantly from previous perturbative approaches.