Dynamical Density-Matrix Renormalization-Group: A New Method To Explore Non-Equilibrium Phenomena In Quantum Dots
Abstract
We extend the density-matrix renormalization-group (DMRG) algorithm(S. R. White, Phys. Rev. B48), 10345 (1993). to analyze the dynamics of electrons in semiconducting quantum dots which are driven out of equilibrium by time-dependent gate potentials. Unlike other approaches, the method is essentially exact, has no spurious divergences, and works equally well for both infinite and finite Coulomb interaction. We model the system with a generalized time-dependent Newns-Anderson Hamiltonian. The DMRG algorithm then effects a systematic truncation of the many-particle Hilbert space, reducing it to manageable size. We thus obtain a representation of the Hamiltonian in the most important part of the Hilbert space. Errors induced by the truncation can be controlled by increasing the size of the retained Hilbert space up to limits on the memory and speed set by the computer. The Schrödinger equation is then integrated forward in time. The special case of spinless electrons furnishes a useful test of the method, as it can be solved exactly; we demonstrate that the dynamical DMRG method is in excellent agreement with exact results. We then study the physically relevant case of spinning electrons and consider the interplay between Kondo and other time scales.
- Publication:
-
APS March Meeting Abstracts
- Pub Date:
- March 2001
- Bibcode:
- 2001APS..MARG33006C