Influence of Dynamics in Interacting Fermion Systems: Ground State Spin of Quantum Dots

Weiss, Yuval

In this dissertation we use sophisticated numerical methods in order to examine ground-state (GS) properties of two types of quantum systems with electron electron interactions: A quantum dot (QD) and a nano-wire. In the first half of the work we study a system of a single level coupled to a one-dimensional wire with interacting spinless electrons, when the wire is either clean or disordered. We utilize the density-matrix renormalization-group (DMRG) method to investigate the influence of the level on several thermodynamic properties of the clean interacting wire, which can be in one of two phases: Tomonaga-Luttinger liquid and charge density wave phases. When the wire is disordered, we investigate the Friedel oscillations, exploring the difference between the two phases and comparing them to the clean non-interacting case, for which we develop an exact formula for the oscillations. In the second half of the dissertation we study two cases of an isolated two-dimensional QD. We begin by an investigation of a new numerical method, the particle-hole DMRG (PH-DMRG), which is used to calculate the GS energy of a disordered QD consisting of interacting spinless electrons. We show that this method is much more accurate than the Hartree-Fock method, and we suggest an improvement of the algorithm, which reduces the error rate by almost 30 percents. Finally we study the magnetization of a QD with spin 1/2 electrons, in the presence of spin-orbit coupling and interactions. We calculate the g-factor and the expectation values of the spin operators in the GS, and find that when the QD is occupied by an even number of electrons, the GS can have a finite magnetization.

Ilya V. Ponomarev, Matt Doty, Michael Scheibner +3 more

M. S. Makivić, Mark Jarrell

Tristan West

This thesis investigates the dynamics of an atomic quantum dot (AQD) coupled to a Bose-Einstein condensate (BEC) via particle exchange and interactions. This is motivated by the possibility of using such a system as a non-destructive probe of the BEC. A review of the physics of a BEC and relevant impurity models is presented. The collisional blockade regime of the AQD is considered, and the AQD is modelled as a spin-1/2 pseudospin. Having expressed the BEC in terms of number and phase, the semi-classical ground state of the system is determined. The fluctuations in number and phase around this ground state are assumed to be small. Using Fermi's golden rule, the decay rates of the system are calculated. The system dynamics are found to be highly dependent on dimensionality and the coupling between AQD and BEC. Having derived the action for this system, it is found that the small phase fluctuation assumption fails in two dimensions and for certain limits in three dimensions. We attempt to circumvent this difficulty using a canonical transformation. The resulting system is related to a biased spin-boson model. Expressing the pseudospin in terms of Schwinger bosons, the self energy for this system is determined. Green's functions for the system are derived by solving Dyson's equation, and a decay rate is extracted. Determining the spin-spin temporal correlation functions by solving the Bethe-Salpeter equation is found to be intractable due to the Schwinger boson number constraint. The possibility of avoiding this problem using the Holstein-Primakoff representation in a large-S generalisation of the AQD states is explored. We find that the pseudospin precession can be controlled by tuning the coupling parameters and the interactions in the BEC. In particular, we found two unexpected regimes where the pseudospin precession can be slowed down to arbitrarily small frequencies.

Nga T. T. Nguyen, François Maria Peeters

The electron-electron correlations in a many-electron $({N}_{e}=1,2,\dots{},5)$ quantum dot confined by a parabolic potential is investigated in the presence of a single magnetic ion and a perpendicular magnetic field. We obtained the energy spectrum and calculated the addition energy which exhibits cusps as a function of the magnetic field. The vortex properties of the many-particle wave function of the ground state are studied and for large magnetic fields are related to composite fermions. The position of the impurity influences strongly the spin-pair-correlation function when the external field is large. In a small applied magnetic field, the spin-exchange energy together with the Zeeman terms leads to a ferromagnetic-antiferromagnetic (FM-AFM) transition. When the magnetic ion is shifted away from the center of the quantum dot, a remarkable re-entrant AFM-FM-AFM transition is found as a function of the strength of the Coulomb interaction. Thermodynamic quantities such as the heat capacity, the magnetization, and the susceptibility are also studied. The cusps in the energy levels show up as peaks in the heat capacity and the susceptibility.

Shainen M. Davidson, Dries Sels, Anatoli Polkovnikov