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Register a new userDensity functional theory for a model quantum dot: Beyond the local-density approximation
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We study both static and transport properties of model quantum dots, employing density functional theory as well as (numerically) exact methods. For the lattice model under consideration the accuracy of the local-density approximation generally is poor. For weak interaction, however, accurate results are achieved within the optimized effective potential method, while for intermediate interaction strengths a method combining the exact diagonalization of small clusters with density functional theory is very successful. Results obtained from the latter approach yield very good agreement with density matrix renormalization group studies, where the full Hamiltonian consisting of the dot and the attached leads has to be diagonalized. Furthermore we address the question whether static density functional theory is able to predict the exact linear conductance through the dot correctly - with, in general, negative answer.
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We propose a computationally efficient approach to the nonadiabatic time-dependent density functional theory (TDDFT) which is based on a representation of the frequency-dependent exchange correlation kernel as a response of a set of damped oscillators. The requirements to computational resources needed to implement our approach do not differ from those of the standard real-time TDDFT in the adiabatic local density approximation (ALDA). Thus, our result offers an exciting opportunity to take into account temporal nonlocality and memory effects in calculations with TDDFT in quantum chemistry and solid state physics for unprecedentedly low costs.
In a previous paper we suggested that a macroscopic force field applied across a two-dimensional electron gas channel could induce a microscopic charge density wave as soon as the proper compressibility becomes negative, which happens at densities much higher than the critical density for the Wigner crystal transition. The suggestion was based on a calculation of the ground state energy in the local density approximation. In this paper we refine our calculation of the energy by including a self-consistent gradient correction to the kinetic energy. Due to the increased energy cost of rapid density variations, we find a much lower critical density for the onset of the charge density wave. This critical density coincides with the result of a linear stability analysis of the uniform ground state in the absence of the electric field.
Localized basis sets in the projector augmented wave formalism allow for computationally efficient calculations within density functional theory (DFT). However, achieving high numerical accuracy requires an extensive basis set, which also poses a fundamental problem for the interpretation of the results. We present a way to obtain a reduced basis set of atomic orbitals through the subdiagonalization of each atomic block of the Hamiltonian. The resulting local orbitals (LOs) inherit the information of the local crystal field. In the LO basis, it becomes apparent that the Hamiltonian is nearly block-diagonal, and we demonstrate that it is possible to keep only a subset of relevant LOs which provide an accurate description of the physics around the Fermi level. This reduces to some extent the redundancy of the original basis set, and at the same time it allows one to perform post-processing of DFT calculations, ranging from the interpretation of electron transport to extracting effective tight-binding Hamiltonians, very efficiently and without sacrificing the accuracy of the results.
It is shown here that the Exact Exchange (EE) formalism provides a natural and rigorous approach for a Density Functional Theory (DFT) of the Integer Quantum Hall Effect (IQHE). Application of a novel EE method to a quasi two-dimensional electron gas (q2DEG) subjected to a perpendicular magnetic field leads to the following main findings. textit{i)} the microscopic exchange energy functional of the IQHE has been obtained, whose main feature being that it minimizes with a discontinuous derivative at every integer filling factor $ u$; textit{ii)} an analytical solution is found for the magnetic-field dependent EE potential, in the one-subband regime; textit{iii)} as a consequence of textit{i)}, the EE potential display sharp discontinuities at every integer $ u$; and textit{iv)} the widely used Local Spin Density Approximation (LSDA) is strongly violated for filling factors close to integer values.
We calculate the nonequilibrium local density of states on a vibrational quantum dot coupled to two electrodes at T=0 using a numerically exact diagrammatic Monte Carlo method. Our focus is on the interplay between the electron-phonon interaction strength and the bias voltage. We find that the spectral density exhibits a significant voltage dependence if the voltage window includes one or more phonon sidebands. A comparison with well-established approximate approaches indicates that this effect could be attributed to the nonequilibrium distribution of the phonons. Moreover, we discuss the long transient dynamics caused by the electron-phonon coupling.
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