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arXiv:1005.3127 · Physical Review Letters

Correlation-Induced Memory Effects in Transport Properties of Low-Dimensional Systems

Enrico Perfetto, Gianluca Stefanucci, Michele Cini

Published Oct 5, 2010• 38 citations
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Abstract

We demonstrate the remnant presence of initial correlations in the steady-state electrical current jS flowing between low-dimensional interacting leads. The leads are described as Luttinger liquids and electrons can tunnel via a quantum point contact. We derive an analytic result for the time-dependent current and show that ground-state correlations have a large impact on the relaxation and long-time behavior. In particular, the I-V characteristic is not reproduced by quenching the interaction in time. We further present a universal formula of jS for an arbitrary sequence of interaction quenches and it is established that jS is history dependent for nonsmooth switching process.

DOI
10.1103/physrevlett.105.156802

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•Jun 1, 2017•0 citations
We demonstrate the remnant presence of initial correlations in the steady-state electrical current jS flowing between low-dimensional interacting leads. The leads are described as Luttinger liquids and electrons can tunnel via a quantum point contact. We derive an analytic result for the time-dependent current and show that ground-state correlations have a large impact on the relaxation and long-time behavior. In particular, the I-V characteristic is not reproduced by quenching the interaction in time. We further present a universal formula of jS for an arbitrary sequence of interaction quenches and it is established that jS is history dependent for nonsmooth switching process.
We study theoretically the memory effects due to different kinds of initial conditions in the transport properties of one-dimensional systems described by the Tomonaga-Luttinger model. We show that in presence of electron–electron interactions the sudden switching of a weak link between two initially uncontacted reservoirs induces a qualitative change in the transient current with respect to the contacted case. In particular the different switching process produces a change in the power-law temporal relaxation of the current towards the steady-state as well as a significant suppression of the transient oscillations. Even more dramatic is the response to a sudden interaction quench, which remarkably leads to a current–voltage characteristic differing from the one displayed if the system was initially interacting.
Strongly correlated transport of interacting electrons through the one-dimensional tunnel contact is considered within the Luttinger liquid model of one-dimensional electrodes on arbitrary time scales t>ħ/Λg. Using previous results, namely, the Self-equilibration theorem proven in Ref. [20] the exact distribution functions P(N,t) for the probabilities of N electrons to tunnel through the contact by the time t are derived and plotted as 3D intensity graphs called real-time tunneling maps in a whole available region of Luttinger liquid correlation parameter values, bias voltages, and temperatures. The tunneling maps being obtained reveal tunneling anomalies - unusually high tunneling probabilities for the small numbers of electrons on the short-time scales beyond the steady state regime of electron tunnel transport. Especially, this concerns the case of strong short-range electron-electron interaction in the leads at g≲1/2. The effect being found can be treated as the direct consequence of the self-equilibration phenomenon. It is shown that features of such an anomalous electron tunneling beyond the steady state regime can be used for precise experimental measurements of small differences between Luttinger liquid correlation parameter values in different one-dimensional quantum-point contacts.
The transport dynamics of a quenched Luttinger liquid tunnel-coupled to a fermionic reservoir is investigated. In the transient dynamics, we show that for a sudden quench of the electron interaction universal power-law decay in time of the tunneling current occurs, ascribed to the presence of entangled compound excitations created by the quench. In sharp contrast to the usual nonuniversal power-law behavior of a zero-temperature nonquenched Luttinger liquid, the steady-state tunneling current is Ohmic and can be explained in terms of an effective quench-activated heating of the system. Our study unveils an unconventional dynamics for a quenched Luttinger liquid that could be identified in quenched cold Fermi gases.
Dynamics of a system in general depends on its initial state and how the system is driven, but in many-body systems the memory is usually averaged out during evolution. Here, interacting quantum systems without external relaxations are shown to retain long-time memory effects in steady states. To identify memory effects, we first show quasi-steady-state currents form in finite, isolated Bose- and Fermi-Hubbard models driven by interaction imbalance and they become steady-state currents in the thermodynamic limit. By comparing the steady-state currents from different initial states or ramping rates of the imbalance, long-time memory effects can be quantified. While the memory effects of initial states are more ubiquitous, the memory effects of switching protocols are mostly visible in interaction-induced transport in lattices. Our simulations suggest that the systems enter a regime governed by a generalized Fick's law and memory effects lead to initial-state-dependent diffusion coefficients. We also identify conditions for enhancing memory effects and discuss possible experimental implications.
We study the relaxation dynamics of the one-dimensional Tomonaga–Luttinger model after an interaction quench, paying particular attention to the momentum dependence of the two-particle interaction. Several potentials of different analytical forms are investigated that all lead to universal Luttinger liquid (LL) physics in equilibrium. The steady-state fermionic momentum distribution shows universal behavior in the sense of the LL phenomenology. For generic regular potentials, the large time decay of the momentum distribution function toward the steady-state value is characterized by a power law with a universal exponent that depends only on the potential at zero momentum transfer. The commonly employed ad hoc procedure fails to give this exponent. In addition to quenches from zero to positive interactions, we also consider the abrupt changes in the interaction between two arbitrary values. Additionally, we discuss the appearance of a factor of two between the steady-state momentum distribution function and that obtained in equilibrium at equal two-particle interaction.
Dynamics of a system generally depends on its initial state and how the system is driven, but in many-body systems the memory is usually averaged out during evolution. Here, interacting quantum systems without external relaxations are shown to retain long-time memory effects in steady states. To identify memory effects, we first show quasi-steady state currents form in finite, isolated Bose and Fermi Hubbard models driven by interaction imbalance and they become steady-state currents in the thermodynamic limit. By comparing the steady state currents from different initial states or ramping rates of the imbalance, long-time memory effects can be quantified. While the memory effects of initial states are more ubiquitous, the memory effects of switching protocols are mostly visible in interaction-induced transport in lattices. Our simulations suggest the systems enter a regime governed by a generalized Fick's law and memory effects lead to initial-state dependent diffusion coefficients. We also identify conditions for enhancing memory effects and discuss possible experimental implications.