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.
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.
We investigate electronic transport through a parallel double quantum dot (DQD) system with strong on-site Coulomb interaction and capacitive interdot coupling. By applying the numerical renormalization group (NRG) method, the ground state of the system and the transmission probability at zero temperature have been obtained. For a system of quantum dots with degenerate energy levels and small interdot tunnel coupling, the spin correlations between the DQDs is ferromagnetic and the ground state of the system is a spin-1 triplet state. The linear conductance will reach the unitary limit (2e(2)/h) due to the underscreened Kondo effect at low temperature. As the interdot tunnel coupling increases, there is a quantum phase transition from ferromagnetic to antiferromagnetic spin correlation in DQDs and the linear conductance is strongly suppressed.
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) x 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.
We investigate electronic transport through a parallel double quantum dot (DQD) system with strong on-site Coulomb interaction, as well as the interdot tunnelling. By applying numerical renormalization group method, the ground state of the system and the transmission probability at zero temperature are obtained. For a system of quantum dots with degenerate energy levels and small interdot tunnel coupling, the spin correlations between the DQDs is ferromagnetic, and the ground state of the system is a spin-1 triplet state. The linear conductance will reach the unitary limit (2 e 2 / h ) due to the Kondo effect at low temperature. As the interdot tunnel coupling increases, there is a quantum phase transition from ferromagnetic to anti-ferromagnetic spin correlation in DQDs and the linear conductance is strongly suppressed.
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.
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 study the ground‐state properties of a triple quantum dot based on a three‐site Hubbard model connected to two non‐interacting leads. Using the numerical renormalization group (NRG), the many‐body phase shifts and dc conductance are calculated away from half‐filling as a function of the onsite energy εd, which corresponds to the gate voltage. The results for conductance g show the typical Kondo plateaus of the Unitary limit g ≈ 2e2/h at some finite ranges of the gate‐voltage corresponding to odd Nel (≈ 1, 3 and 5), where Nel is the total number of electrons in the triple dot. The conductance shows broad minima for even Nel(≈ 2 and 4). The local charge Nel shows a staircase behavior as a function of εd.