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APS

Dynamical Density-Matrix Renormalization-Group: A New Method To Explore Non-Equilibrium Phenomena In Quantum Dots

Miguel A. Cazalilla, Brad Marston

Published Mar 1, 2001• 0 citations
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The density-matrix renormalization-group algorithm is extended to treat time-dependent problems. The method provides a systematic and robust tool to explore out-of-equilibrium phenomena in quantum many-body systems. We illustrate the method by showing that attractive interactions enhance the tunneling current between two Luttinger liquids, whereas repulsive interactions suppress it, in qualitative agreement with analytical predictions. Enhancement of the transport current through a quantum dot in the Kondo regime is also exhibited.
We present a new method for the numerical calculation of the equilibrium crystal shape around a facet. Our method is based on the transfer matrix method with the product-wave-function renormalization group (PWFRG) algorithm for the asymmetric density matrix, which is an extension of the density matrix renormalization group (DMRG) algorithm. By applying this method to the staggered body-centered-cubic solid-on-solid model, which is known to exhibit the inverse roughening phenomena, we obtain the facet shape, shape exponents, and step tension.
A new application of the density matrix renormalization group (DMRG) method to a system composed of an interacting dot coupled to a infinite one dimensional lead is presented. This method enables one to study the influence of the coupling to an external lead on the thermodynamical properties of the dot. It is shown that this method reproduces known results for a non-interacting dot coupled to a lead, i.e., that for strong coupling discrete states remain in the dot. We show that these states are robust and do not disappear once interactions in the dot are considered. Moreover, due to these discrete states, Coulomb blockade affects the charging of the dot even though its strongly coupled to a lead.