arXiv:0903.3344 · Physical Review B

Transient dynamics of the nonequilibrium Majorana resonant level model

A. Komnik

Published Jun 1, 2009• 28 citations

Abstract

The Majorana resonant level model describes the universality class of the two-channel/terminal Kondo model at the Toulouse point as well as of a resonant level between two half-infinite Tomonaga-Luttinger liquids. We analyze the time evolution of the electric current and of the population function after an instantaneous switching on of the tunneling coupling. We find that the only time scale, which governs the relaxation of the initial dot preparation is the inverse contact transparency $\ensuremath{\Gamma}$, whatever the dot offset energy $\ensuremath{\Delta}$, applied bias voltage, or temperature. The voltage alone determines the superimposed oscillatory behavior of the observables for weak detuning $|\ensuremath{\Delta}|<\ensuremath{\Gamma}/2$. In the opposite case of strong detuning $|\ensuremath{\Delta}|>\ensuremath{\Gamma}/2$ a beating pattern emerges. For the current the finite temperature plays the similar role as the hybridization. The dot population function dynamics approaches that of a resonant $(\ensuremath{\Delta}=0)$ setup upon increasing the voltage or/and temperature.

DOI: 10.1103/physrevb.79.245102

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arXiv:0903.3344 · Physical Review B

Transient dynamics of the nonequilibrium Majorana resonant level model

A. Komnik

Published Jun 1, 2009• 28 citations

arXiv HTML PDF

Abstract

\ensuremath{\Gamma}

, whatever the dot offset energy

\ensuremath{\Delta}

, applied bias voltage, or temperature. The voltage alone determines the superimposed oscillatory behavior of the observables for weak detuning

|\ensuremath{\Delta}|<\ensuremath{\Gamma}/2

. In the opposite case of strong detuning

|\ensuremath{\Delta}|>\ensuremath{\Gamma}/2

a beating pattern emerges. For the current the finite temperature plays the similar role as the hybridization. The dot population function dynamics approaches that of a resonant

(\ensuremath{\Delta}=0)

setup upon increasing the voltage or/and temperature.

DOI: 10.1103/physrevb.79.245102

Related papers

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arXiv:1211.3748Physical Review BJun 21, 201311 citations

\ensuremath{\Gamma}

, whatever the dot offset energy

\ensuremath{\Delta}

, applied bias voltage, or temperature. The voltage alone determines the superimposed oscillatory behavior of the observables for weak detuning

|\ensuremath{\Delta}|<\ensuremath{\Gamma}/2

. In the opposite case of strong detuning

|\ensuremath{\Delta}|>\ensuremath{\Gamma}/2

a beating pattern emerges. For the current the finite temperature plays the similar role as the hybridization. The dot population function dynamics approaches that of a resonant

(\ensuremath{\Delta}=0)

setup upon increasing the voltage or/and temperature.

The equilibrium physics of quantum impurities frequently involves a universal crossover from weak to strong reservoir-impurity coupling, characterized by single-parameter scaling and an energy scale

{T}_{K}

(Kondo temperature) that breaks scale invariance. For the noninteracting resonant level model, the nonequilibrium time evolution of the Loschmidt echo after a local quantum quench was recently computed explicitly [R. Vasseur, K. Trinh, S. Haas, and H. Saleur, Phys. Rev. Lett. 110, 240601 (2013)]. It shows single-parameter scaling with variable

{T}_{K}t

. Here, we scrutinize whether similar universal dynamics can be observed in various interacting quantum impurity systems. Using density matrix and functional renormalization group approaches, we analyze the time evolution resulting from abruptly coupling two noninteracting Fermi or interacting Luttinger liquid leads via a quantum dot or a direct link. We also consider the case of a single Luttinger liquid lead suddenly coupled to a quantum dot. We investigate whether the field-theory predictions for the universal scaling as well as for the large-time behavior successfully describe the time evolution of the Loschmidt echo and the entanglement entropy of microscopic models. Our study shows that for the considered local quench protocols the above quantum impurity models fall into a class of problems for which the nonequilibrium dynamics can largely be understood based on the knowledge of the corresponding equilibrium physics.

V

. In the linear-response regime $V\ensuremath{\rightarrow}0$, the system exhibits as a function of the dissipative strength a localized-delocalized quantum transition of the Kosterlitz-Thouless (KT) type. We address fundamental issues of the nonequilibrium transport near the quantum phase transition: Does the bias voltage play the same role as temperature to smear out the transition? What is the scaling of the nonequilibrium conductance near the transition? At finite temperatures, we show that the conductance follows the equilibrium scaling for

V<T

, while it obeys a distinct nonequilibrium profile for

V>T

. We furthermore provide different signatures of the transition in the finite-frequency current noise and ac conductance via a recently developed functional renormalization group (FRG) approach. The generalization of our analysis to nonequilibrium transport through a resonant level coupled to two chiral Luttinger liquid leads, generated by fractional quantum Hall edge states, is discussed. Our work on the dissipative resonant level has direct relevance to experiments on a quantum dot coupled to a resistive environment, such as H. Mebrahtu et al., [Nature (London) 488, 61 (2012)].