Two-channel Kondo phases and frustration-induced transitions in triple quantum dots

TL;DR

This paper investigates the complex quantum phases and transitions in a triple quantum dot system coupled to metallic leads, revealing multiple two-channel Kondo phases, a frustration-induced quantum phase transition, and a critical point characterized by unique low-energy behavior.

Contribution

It introduces a detailed analysis of frustration-induced quantum phase transitions and multiple 2CK phases in a triple quantum dot system, with a derived effective low-energy model and numerical validation.

Findings

Identification of two distinct 2CK phases with different ground state parities.

Discovery of a frustration-induced quantum phase transition separating these phases.

Characterization of the critical fixed point with a free pseudospin and 1-channel spin quenching.

Abstract

We consider a ring of three quantum dots mutually coupled by antiferromagnetic exchange interactions, and tunnel-coupled to two metallic leads: the simplest device in which the consequences of local frustration arising from internal degrees of freedom may be studied within a 2-channel environment. Two-channel Kondo (2CK) physics is found to predominate at low-energies in the mirror-symmetric systems considered, with a residual spin 1/2 overscreened by coupling to both leads. It is however shown that two distinct 2CK phases, with different ground state parities, arise on tuning the interdot exchange couplings. In consequence a frustration-induced quantum phase transition occurs, the 2CK phases being separated by a quantum critical point for which an effective low-energy model is derived. Precisely at the transition, parity mixing of the quasi-degenerate local trimer states acts to destabilise the 2CK fixed points; and the critical fixed point is shown to consist of a free pseudospin together with effective 1-channel spin quenching, itself reflecting underlying channel-anisotropy in the inherently 2-channel system. Numerical renormalization group techniques and physical arguments are used to obtain a detailed understanding of the problem, including study of both thermodynamic and dynamical properties of the system.