Kondo Problems in Tomonaga-Luttinger liquids

TL;DR

This paper reviews quantum impurity problems in Tomonaga-Luttinger liquids, highlighting their analogy to the Kondo problem, and discusses impurity effects, orthogonality catastrophe, and impurity screening in one-dimensional interacting electron systems.

Contribution

It provides a comprehensive review of Kondo problems in TLLs, emphasizing the effects of impurities and the screening phenomena in one-dimensional correlated systems.

Findings

Repulsive interactions effectively cut the TLL into two parts.

Orthogonality catastrophe occurs in TLLs.

Impurity spin is fully screened in the Kondo effect within TLLs.

Abstract

Quantum impurity problems in Tomonaga-Luttinger liquids (TLLs) are reviewed with emphasis on their analogy to the Kondo problem in Fermi liquids. First, the problem of a static impurity in a spinless TLL is considered, which is related to the model studied in the context of the macroscopic quantum coherence. In the low-energy limit the TLL is essentially cut into two pieces when interaction is repulsive. The orthogonality catastrophe in a TLL is then discussed. Finally, the Kondo effect of a spin-1/2 impurity in a one-dimensional repulsively interacting electron liquids (a spinful TLL) is reviewed. Regardless of the sign of the exchange coupling, the impury spin is completely screened in the ground state. The leading low-temperature contributions to thermodynamic quantities come from boundary contributions of a bulk leading irrelevant operator.