The role of impurities in quantum dot quantum computers

Bruno Max de Souza Melo

The single impurity Anderson model (SIAM) is one of the most recurrent model Hamiltonians in condensed matter physics, playing an important role in the description of systems where electron-electron interactions can not be neglected, such as strongly interacting quantum dots and doped metals with magnetic impurities. In order to address the variety of scenarios in which the model can be applied many impurity solvers were developed for the SIAM. It is consensus that there is no universal method that provides reliable results for the model parameter space of experimental interest. The main methods found in the literature di ers signi cantly on the computational cost involved in the numerical implementation and in the range of the model parameters where the used method is reliable. In this undergraduate dissertation we study the reliability of some impurity solvers for the SIAM, namely, the equations of motion (EOM) method, the numerical renormalization group (NRG), the non-crossing approximation (NCA), and the one crossing approximation (OCA). We study the Green's function of a quantum dot using the aforementioned impurity solvers and then calculate the density of states as a function of the temperature and the chemical potential of the quantum dot . Our analysis is focused on the Coulomb blockade and the Kondo physics. We report that some standard approximations based on the EOM technique display a rather unexpected poor behaviour in the Coulomb blockade regime even at high temperatures.

Daniel Loss

哲夫 小寺, Tetsuo Kodera

Hong Yu Gong, Arif Ullah, LvZhou Ye +2 more

Quantum dots comprise a type of quantum impurity system. The entanglement and coherence of quantum states are significantly influenced by the strong electron-electron interactions among impurities and their dissipative coupling with the surrounding environment. Competition between many-body effects and transfer couplings plays an important role in determining the entanglement among localized impurity spins. In this work, we employ the hierarchical-equations-of-motion approach to explore the entanglement of a strongly correlated double quantum dots system. The relation between the total system entropy and those of subsystems is also investigated.

Surajit Saha, Manas Ghosh

弘理 笹倉