arXiv:cond-mat/0601411 · Physical Review B

Adaptive time-dependent density-matrix renormalization-group technique for calculating the conductance of strongly correlated nanostructures

K. A. Al-Hassanieh, Adrian E. Feiguin, José A. Riera, C. A. Büsser, Elbio R. Dagotto

Published May 3, 2006• 87 citations

Abstract

A procedure based on the recently developed ``adaptive'' time-dependent density-matrix-renormalization-group (DMRG) technique is presented to calculate the zero temperature conductance of nanostructures, such as quantum dots (QDs) or molecular conductors, when represented by a small number of active levels. The leads are modeled using noninteracting tight-binding Hamiltonians. The ground state at time zero is calculated at zero bias. Then, a small bias is applied between the two leads, the wave function is DMRG evolved in time, and currents are measured as a function of time. Typically, the current is expected to present periodicities over long times, involving intermediate well-defined plateaus that resemble steady states. The conductance can be obtained from those steady-state-like currents. To test this approach, several cases of interacting and noninteracting systems have been studied. Our results show excellent agreement with exact results in the noninteracting case. More importantly, the technique also reproduces quantitatively well-established results for the conductance and local density of states in both the cases of one and two coupled interacting QDs. The technique also works at finite bias voltages, and it can be extended to include interactions in the leads.

DOI: 10.1103/physrevb.73.195304

Related papers

Time-Dependent DMRG Study on Quantum Dot under a Finite Bias Voltage

Shunsuke Kirino, Tatsuya Fujii, Jize Zhao +1 more

Resonant tunneling through quantum dot under a finite bias voltage at zero temperature is investigated by using the adaptive time-dependent density matrix renormalization group(TdDMRG) method. Quantum dot is modeled by the Anderson Hamiltonian with the 1-D nearest-neighbor tight-binding leads. Initially the ground state wave function is calculated with the usual DMRG method. Then the time evolution of the wave function due to the slowly changing bias voltage between the two leads is calculated by using the TdDMRG technique. Even though the system size is finite, the expectation values of current operator show steady-like behavior for a finite time interval, in which the system is expected to resemble the real nonequilibrium steady state of the infinitely long system. We show that from the time intervals one can obtain quantitatively correct results for differential conductance in a wide range of bias voltage. Finally we observe an anomalous behavior in the expectation value of the double occupation operator at the dot $$ as a function of bias voltage.

arXiv:0805.0218Journal of the Physical Society of JapanJul 25, 200848 citations

Transport properties and Kondo correlations in nanostructures: Time-dependent DMRG method applied to quantum dots coupled to Wilson chains

Luis G. G. V. Dias da Silva, Fabian Heidrich‐Meisner, Adrian E. Feiguin +4 more

We apply the adaptive time-dependent density-matrix renormalization-group method (tDMRG) to the study of transport properties of quantum-dot systems connected to metallic leads. Finite-size effects make the usual tDMRG description of the Kondo regime a numerically demanding task. We show that such effects can be attenuated by describing the leads by ``Wilson chains,'' in which the hopping matrix elements decay exponentially away from the impurity $({t}_{n}\ensuremath{\propto}{\ensuremath{\Lambda}}^{\ensuremath{-}n/2})$. For a given system size and in the linear-response regime, results for $\ensuremath{\Lambda}>1$ show several improvements over the undamped $\ensuremath{\Lambda}=1$ case: perfect conductance is obtained deeper in the strongly interacting regime and current plateaus remain well defined for longer time scales. Similar improvements were obtained in the finite-bias regime up to bias voltages of the order of the Kondo temperature. These results show that with the proposed modification, the tDMRG characterization of Kondo correlations in the transport properties can be substantially improved, while it turns out to be sufficient to work with much smaller system sizes. We discuss the numerical cost of this approach with respect to the necessary system sizes and the entanglement growth during the time evolution.

arXiv:0807.0581Physical Review BNov 19, 200888 citations

Conductance of correlated systems: real-time dynamics in finite systems

Alexander Branschädel, Guenter Schneider, Peter Schmitteckert

Numerical time evolution of transport states using time dependent Density Matrix Renormalization Group (td-DMRG) methods has turned out to be a powerful tool to calculate the linear and finite bias conductance of interacting impurity systems coupled to non-interacting one-dimensional leads. Several models, including the Interacting Resonant Level Model (IRLM), the Single Impurity Anderson Model (SIAM), as well as models with different multi site structures, have been subject of investigations in this context. In this work we give an overview of the different numerical approaches that have been successfully applied to the problem and go into considerable detail when we comment on the techniques that have been used to obtain the full I--V-characteristics for the IRLM. Using a model of spinless fermions consisting of an extended interacting nanostructure attached to non-interacting leads, we explain the method we use to obtain the current--voltage characteristics and discuss the finite size effects that have to be taken into account. We report results for the linear and finite bias conductance through a seven site structure with weak and strong nearest-neighbor interactions. Comparison with exact diagonalisation results in the non-interacting limit serve as a verification of the accuracy of our approach. Finally we discuss the possibility of effectively enlarging the finite system by applying damped boundaries and give an estimate of the effective system size and accuracy that can be expected in this case.

arXiv:1004.4178Apr 23, 20100 citations

Conductance in strongly correlated 1D systems: Real-Time Dynamics in DMRG

Schneider, Guenter, Peter Schmitteckert

A new method to perform linear and finite bias conductance calculations in one dimensional systems based on the calculation of real time evolution within the Density Matrix Renormalization Group (DMRG) is presented. We consider a system of spinless fermions consisting of an extended interacting nanostructure attached to non-interacting leads. Results for the linear and finite bias conductance through a seven site structure with weak and strong nearest-neighbor interactions are presented. Comparison with exact diagonalization results in the non-interacting limit serve as verification of the accuracy of our approach. Our results show that interaction effects lead to an energy dependent self energy in the differential conductance.

arXiv:cond-mat/0601389Jan 17, 200611 citations

Conductance of inhomogeneous systems: Real‐time dynamics

Alexander Branschädel, G. Schneider, Peter Schmitteckert

Abstract Numerical time evolution of transport states using time dependent Density Matrix Renormalization Group (td‐DMRG) methods has turned out to be a powerful tool to calculate the linear and finite bias conductance of interacting impurity systems coupled to non‐interacting one‐dimensional leads. Several models, including the Interacting Resonant Level Model (IRLM), the Single Impurity Anderson Model (SIAM), as well as models with different multi site structures, have been subject of investigations in this context. In this work we give an overview of the different numerical approaches that have been successfully applied to the problem and go into considerable detail when we comment on the techniques that have been used to obtain the full I–V‐characteristics for the IRLM. Using a model of spinless fermions consisting of an extended interacting nanostructure attached to non‐interacting leads, we explain the method we use to obtain the current–voltage characteristics and discuss the finite size effects that have to be taken into account. We report results for the linear and finite bias conductance through a seven site structure with weak and strong nearest‐neighbor interactions. Comparison with exact diagonalisation results in the non‐interacting limit serve as a verification of the accuracy of our approach. Finally we discuss the possibility of effectively enlarging the finite system by applying damped boundaries and give an estimate of the effective system size and accuracy that can be expected in this case.

Annalen der PhysikJul 6, 201067 citations

Applications of the density matrix renormalization group to mesoscopic phenomena

Dominique Gobert, Ulrich Schollwöck

In this thesis, I analyze properties of mesoscopic systems that exhibit strong quantum correlations. To this purpose, I adapt and use the density-matrix renormalization group (DMRG), a numerical method that has been developed specifically for analyzing such systems. The following systems are discussed: - Josephson effect between superconducting nanograins: I investigate the Josephson effect, i.e. the dependence of the energy of two weakly coupled superconductors on the difference between their superconducting phase, in the regime that the level spacing d is comparable to the bulk superconducting gap Delta. Because the BCS solution is inapplicable in this regime, I use the DMRG to calculate the ground state of the two coupled superconductors and extract the Josephson energy E_J. The standard BCS result for E_J is reproduced only in the continuum limit of vanishing d. As d is increased, however, E_J turns out to display a nonmonotonic behaviour. A tight-binding approximation for weak Josephson coupling explains the physical mechanism underlying this reentrance in a transparent way. - Well-defined quasiparticles in small metallic grains: I analyze zero-temperature spectral functions of mesoscopic systems such as quantum dots and metallic grains, in the limit of large conductance, where they can be described by a "universal Hamiltonian" model. I show that within this model, an important class of spectral functions is dominated by one single energy eigenstate only. For an interacting system this is a very peculiar property, which implies an infinite lifetime of the quasiparticles. Moreover, I show that the dominating eigenstate contains only a limited subclass of all excitations, which I characterize as the "No-Gaudino" excitations. Hence, these are sufficient to explain many of the properties of the systems under consideration. Besides its own physical significance, the dominance of the "No-Gaudino" states has also high practical value, because it permits the calculation of zero-temperature spectral functions with high accuracy using the DMRG. I illustrate the use of this method by calculating the tunneling density of states of metallic grains and the magnetic response of mesoscopic rings. - Real-time dynamics in spin-1/2 chains I study the nonequilibrium transport properties in spin-1/2 chains by solving the time evolution of a non-stationary initial state, and investigate the influence of different interaction strength and dimerization on the magnetization transport. To this purpose, I use the "adaptive time-dependent DMRG", a DMRG variant that was recently developed to solve the many-body Schroedinger equation with high accuracy. I find that the magnetization possesses a well-defined long-time limit, whose nature does not depend on the dimerization, but only on the strength J_z of the S^z-S^z-interaction: For |J_z| < 1 I find ballistic magnetization transport, and for J_z >1 almost no transport, with a sharp crossover at |J^z|=1. I explain this crossover as a subtle consequence of a quantum phase transition which occurs at the precise value J_z| = 1. - Many-body scattering states: I present a general method for calculating many-body scattering states that does not rely on the assumptions of perturbation theory or near-equilibrium. Due to the complexity of the problem, I limit the discussion to a description of the algorithm itself and a few proof-of-principle calculations only. The strategy is to calculate the many-body scattering state that results when a scatterer (e.g. a quantum dot) is connected to two leads, to which a voltage bias V is applied. This state is obtained by solving the many-body Lippmann-Schwinger equation using the DMRG.

Jan 1, 20051 citation