We analyze the quantum entanglement between opposite spin projection electrons in the ground state of the Anderson impurity model. In this model, a single level impurity with intralevel repulsion U is tunnel coupled to a free electron gas. The Anderson model presents a strongly correlated many body ground state with mass enhanced quasiparticle excitations. We find, using both analytical and numerical tools, that the quantum entanglement between opposite spin projection electrons is a monotonic universal function of the quasiparticle mass enhancement Z. The mass enhancement, which is used to quantify the correlations in quantum many body systems, could therefore be used to quantify spin entanglement.
We analyze the electronic properties of interacting crystal field split three band systems. Using a rotationally invariant slave boson approach we analyze the behavior of the electronic mass renormalization as a function of the intralevel repulsion $U$, the Hunds coupling $J$, the crystal field splitting, and the number of electrons per site $n$. We first focus on the case in which two of the bands are identical and the levels of the third one are shifted by $Delta>0$ with respect to the former. We find an increasing quasiparticle mass differentiation between the bands, for system away from half-filling ($n=3$), as the Hubbard interaction $U$ is increased. This leads to orbital selective Mott transitions where either the higher energy band (for $4>n>3$) or the lower energy degenerate bands ($2<n<3$) become insulating for $U$ larger than a critical interaction $U_{c}(n)$. Away from the half-filled case $|n-3|gtrsim 0.3$ there is a wide range of parameters for $U<U_c(n)$ where the system presents a Hunds metal phase with the physics dominated by the local high spin multiplets. Finally, we study the fate of the $n=2$ Hunds metal as the energy splitting between orbitals is increased for different possible crystal distortions. We find a strong sensitivity of the Hunds metal regime to crystal fields due to the opposing effects of $J$ and the crystal field splittings on the charge distribution between the bands.
We analyze the linear thermoelectric transport properties of devices with three quantum dots in a star configuration. A central quantum dot is tunnel-coupled to source and drain electrodes and to two additional quantum dots. For a wide range of parameters, in the absence of an external magnetic field, the system is a singular Fermi liquid with a non-analytic behavior of the electric transport properties at low energies. The singular behavior is associated with the development of a ferromagnetic or an underscreened Kondo effect, depending on the parameter regime. A magnetic field drives the system into a regular Fermi liquid regime and leads to a large peak ($sim k_B/|e|$) in the spin thermopower as a function of the temperature, and to a $sim 100%$ spin polarized current for a wide range of parameters due to interference effects. We find a qualitatively equivalent behavior for systems with a larger number of side coupled quantum dots, with the maximum value of the spin thermopower decreasing as the number of side-coupled quantum dots increases.
We calculate the photoluminescence spectrum of a single semiconductor quantum dot strongly coupled to a continuum as a function of light frequency, gate voltage, and magnetic field. The spectrum is dominated by the recombination of several excitonic states which can be considered as quantum quenchs in which the many-body nature of the system is suddenly changed between initial and final states. This is associated with an Anderson orthogonality catastrophe with a power-law singularity at the threshold. We explain the main features observed experimentally in the region of stability of the trion $X^-$, the neutral exciton $X^0$ and the gate voltage induced transition between them.
The dynamical mean field theory (DMFT) has become a standard technique for the study of strongly correlated models and materials overcoming some of the limitations of density functional approaches based on local approximations. An important step in this method involves the calculation of response functions of a multiorbital impurity problem which is related to the original model. Recently there has been considerable progress in the development of techniques based on the density matrix renormalization group (DMRG) and related matrix product states (MPS) implying a substantial improvement to previous methods. In this article we review some of the standard algorithms and compare them to the newly developed techniques, showing examples for the particular case of the half-filled two-band Hubbard model.
We analyze the low energy properties of a device with $N+1$ quantum dots in a star configuration. A central quantum dot is tunnel coupled to source and drain electrodes and to $N$ quantum dots. Extending previous results for the $N=2$ case we show that, in the appropriate parameter regime, the low energy Hamiltonian of the system is a ferromagnetic Kondo model for a $S=(N-1)/2$ impurity spin. For small enough interdot tunnel coupling, however, a two-stage Kondo effect takes place as the temperature is decreased. The spin $1/2$ in the central quantum dot is Kondo screened first and at lower temperatures the antiferromagnetic coupling to the side coupled quantum dots leads to an underscreened $S=N/2$ Kondo effect. We present numerical results for the thermodynamic and spectral properties of the system which show a singular behavior at low temperatures and allow to characterize the different strongly correlated regimes of the device.
We analyze the transport properties of a double quantum dot device in the side-coupled configuration. A small quantum dot (QD), having a single relevant electronic level, is coupled to source and drain electrodes. A larger QD, whose multilevel nature is considered, is tunnel-coupled to the small QD. A Fermi liquid analysis shows that the low temperature conductance of the device is determined by the total electronic occupation of the double QD. When the small dot is in the Kondo regime, an even number of electrons in the large dot leads to a conductance that reaches the unitary limit, while for an odd number of electrons a two stage Kondo effect is observed and the conductance is strongly suppressed. The Kondo temperature of the second stage Kondo effect is strongly affected by the multilevel structure of the large QD. For increasing level spacing, a crossover from a large Kondo temperature regime to a small Kondo temperature regime is obtained when the level spacing becomes of the order of the large Kondo temperature.
