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

TL;DR

This paper uses time-dependent DMRG to study quantum dot transport under bias voltage, revealing steady-state behavior and conductance characteristics, along with an anomalous double occupation response.

Contribution

It introduces a time-dependent DMRG approach to analyze nonequilibrium steady states in quantum dots under bias voltage, providing quantitative conductance results.

Findings

Steady-like current behavior observed in finite systems.

Quantitative differential conductance obtained across bias voltages.

Anomalous bias dependence of double occupation at the quantum dot.

Abstract

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 $<n_{\uparrow} n_{\downarrow}>$ as a function of bias voltage.