We consider a triple quantum dot system in a triangular geometry with one of the dots connected to metallic leads. Using Wilson’s numerical renormalization group method, we investigate quantum entanglement and its relation to the thermodynamic and transport properties in the regime where each of the dots is singly occupied on average, but with non-negligible charge fluctuations. It is shown that even in the regime of significant charge fluctuations the formation of the Kondo singlets induces switching between separable and perfectly entangled states. The quantum phase transition between unentangled and entangled states is analyzed quantitatively and the corresponding phase diagram is explained by exactly solvable spin model. In the framework of an effective model we also explain smearing of the entanglement transition for cases when the symmetry of the triple quantum dot system is relaxed.
We consider a triple quantum dot system in a triangular geometry with one of the dots connected to metallic leads. Using Wilson’s numerical renormalization group method, we investigate quantum entanglement and its relation to the thermodynamic and transport properties in the regime where each of the dots is singly occupied on average, but with non-negligible charge fluctuations. It is shown that even in the regime of significant charge fluctuations the formation of the Kondo singlets induces switching between separable and perfectly entangled states. The quantum phase transition between unentangled and entangled states is analyzed quantitatively and the corresponding phase diagram is explained by exactly solvable spin model. In the framework of an effective model we also explain smearing of the entanglement transition for cases when the symmetry of the triple quantum dot system is relaxed.
We investigate a system of three tunnel-coupled semiconductor quantum dots in a triangular geometry, one of which is connected to a metallic lead, in the regime where each dot is essentially singly occupied. Both ferromagnetic and antiferromagnetic spin-21 Kondo regimes, separated by a quantum phase transition, are shown to arise on tuning the interdot tunnel couplings and should be accessible experimentally. Even in the ferromagnetically-coupled local moment phase, the Kondo effect emerges in the vicinity of the transition at finite temperatures. Physical arguments and numerical renormalization group techniques are used to obtain a detailed understanding of the problem.
Semiconductor quantum dot structure provides a promising basis for quantum information processing, within which to reveal the quantum phase and charge transport is one of the most important issues. In this paper, by means of the numerical renormalization group technique, we study the quantum phase transition and the charge transport for a parallel triple dot device in the strongly correlated limit, focusing on the effect of inter-dot hopping t beyond the Kondo regime. We find the quantum behaviors depend closely on the initial electron number on the dots, and the present model may map to single, double, and side-coupled impurity models in different parameter spaces. An orbital spin-1/2 Kondo effect between the conduction leads and the bonding orbital, and several magnetic-frustration phases are demonstrated when t is adjusted to different regimes. To understand these phenomena, a canonical transformation of the energy levels is given, and important physical quantities with respect to increasing t and necessary theoretical discussions are shown.
We consider the simplest example of a double quantum dot system: two equivalent, capacitively coupled single-level dots, each coupled to its own lead. Focussing on a regime of two electrons on the double dot, a rich range of behaviour is found on increasing the interdot coupling: first a crossover from spin- to charge-Kondo physics, via an intermediate SU(4) state with entangled spin and charge degrees of freedom; followed by a quantum phase transition of Kosterlitz-Thouless type to a non-Fermi liquid 'charge-ordered' phase with finite residual entropy and anomalous transport properties. The numerical renormalization group method, coupled with simple physical arguments, is employed to obtain a detailed understanding of the problem.
Using Wilson's numerical renormalization group (NRG) technique we compute zero-bias conductance and various correlation functions of a double quantum dot (DQD) system. We present different regimes within a phase diagram of the DQD system. By introducing a negative Hubbard U on one of the quantum dots, we simulate the effect of electron-phonon coupling and explore the properties of the coexisting spin and charge Kondo state. In a triple quantum dot (TQD) system a multi-stage Kondo effect appears where localized moments on quantum dots are screened successively at exponentially distinct Kondo temperatures.
The transport property and phase transition for a parallel triple dot device are studied by adopting Wilson's numerical renormalization group technique, focusing on the effects of level spacings between neighboring dot sites. By keeping dot 2 at the half-filled level and tuning the level differences, it is demonstrated that the system transits from local spin quadruplet to triplet and doublet sequently, and three kinds of Kondo peaks at the Fermi surface could be found, which are separated by two Kosterlitz–Thouless type quantum phase transitions and correspond to spin–3/2, spin–1, and spin–1/2 Kondo effect, respectively. To obtain a detailed understanding of these problems, the charge occupation, the spin—spin correlation, the transmission coefficient, and the temperature-dependent magnetic moment are shown, and necessary physical arguments are given.
Abstract. The numerical renormalization group is employed to study a double quantum (DQD) dot system consisting of two equivalent single-level dots, each coupled to its own lead and with a mutual capacitive coupling embodied in an interdot interaction U ′, in addition to the intradot Coulomb interaction U. We focus on the regime with two electrons on the DQD, and the evolution of the system on increasing U ′/U. The spin-Kondo effect arising for U ′ = 0 (SU(2) × SU(2)) is found to persist robustly with increasing U ′/U, before a rapid but continuous crossover to (a) the SU(4) point U ′ = U where charge and spin degrees of freedom are entangled and the Kondo scale strongly enhanced; and then (b) a charge-Kondo state, in which a charge-pseudospin is quenched on coupling to the leads/conduction channels. A quantum phase transition of Kosterlitz-Thouless type then occurs from this Fermi liquid, strong coupling (SC) phase, to a broken symmetry, non-Fermi liquid charge ordered (CO) phase at a critical U ′ c. Our emphasis in this paper is on the structure, stability and flows between the underlying RG fixed points, on the overall phase diagram in the (U, U ′)-plane and evolution of the characteristic low-energy Kondo scale inherent to the SC phase; and on static physical properties such as spin- and charge-susceptibilities (staggered and uniform), including universality and scaling behaviour in the strongly correlated regime. Some exact results for associated Wilson ratios are also obtained.