Quantum phase transitions in models of coupled magnetic impurities

Abstract

We discuss models of interacting magnetic impurities coupled to a metallic host. If twice the sum of the impurity spins is larger than the total number of host screening channels, the system shows one or more quantum phase transitions where the ground-state spin changes as a function of the inter-impurity couplings. The simplest example is realized by two spin-1/2 Kondo impurities coupled to a single orbital of the host; this model exhibits a singlet-doublet transition. We investigate the phase diagram and crossover behavior of this model and present Numerical Renormalization Group results together with general arguments showing that the quantum phase transition is either of first order or of the Kosterlitz-Thouless type, depending on the symmetry of the Kondo couplings. Connections to other models and possible applications are discussed.Comment: 4 pages, 3 figs. (v2) Minor changes and clarifications, small asymmetry case discussed; application to multilevel quantum dots emphasized, in particular to the experiment of W. G. van der Wiel et al., cond-mat/0110432, where indications for a Kosterlitz-Thouless-type transition in a multilevel dot are found. Final version as publishe

Entanglement switching via the Kondo effect in triple quantum dots

“…The two regimes are separated by a first order quantum phase transition (level crossing) as a function of t 2 /t 1 which determines the ground state of the isolated TQD [35,37,38,41]. The same quantum phase transition has been previously found in a double quantum dot (DQD) system modeled as a pure spin system [55]. Entanglement properties of a qubit pair formed by spins on adjacent quantum dots are closely related to the spin-spin correlations [26,27] therefore transitions between different spin configurations play a crucial role.…”

“…Critical interdot coupling t 2c is equal to t 1 for decoupled quantum dots, Γ = 0, and is slightly renormalized due to the coupling to the leads [35,37,38,55]. For increasingly large coupling t 2 , the spin-spin correlations diminish due to charge fluctuations, Figure 2d, which reduce the probability for single occupation of the dots, Figure 2c.…”

Universal transport signatures in two-electron molecular quantum dots: gate-tunable Hund’s rule, underscreened Kondo effect and quantum phase transitions

“…1) is the sign of a possible quantum phase transition between two different sorts of ground states. From the identification of the singlet and triplet magnetic states performed in section 2.1, and the confirmation that a single screening channel is active (see discussion in sections 2.2 and 2.3), the obvious scenario to follow is the so-called singlet-triplet unscreening transition [26,27,28,31,32]. In this picture, the transition is driven by the merging of singlet and (underscreened) triplet magnetic excitations together at a quantum critical point.…”

“…7. The physical interpretation of these data is the following [27,28,29,30,31,32,33,34]: at high-temperatures, the two-orbitals act basically as two decoupled spin S = 1/2, and the most strongly coupled spin undergoes a first screening process associated to a Kondo scale T K,S=1/2 , while the more weakly coupled spin remains essentially free. This is witnessed in Fig.…”

“…One can then naturally wonder about the fate of a singlet to degenerate triplet crossing in the presence of a single screening channel [26,27,28,29,30,31,32,33,34], which can in principle be expected for lateral quantum dots [35,36] and molecular devices [34].…”