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Transport Properties as a Tool to Study Universal Quench-induced Dynamics in 1D Systems

Alessio Calzona, Filippo Maria Gambetta, Matteo Carrega, Maura Sassetti

Published Aug 7, 2017• 0 citations
OpenAlex

Abstract

The study of the relaxation process that follows a quantum quench in 1D systems still represents an open research field. Here we consider a sudden change of the interparticle interaction and we identify a peculiar correlator of the system whose behavior is directly and deeply affected by the quench-induced dynamics. Interestingly, it features a universal power-law decay in time. Unfortunately, such a universal decay, although present, turns out to be subleading in intrinsic properties of the system such as the non- equilibrium spectral function. We thus consider a tunnel coupling of the system with a biased tip in order to be able to study also transport properties, namely the charge and energy current flowing from the tip to the system after the quench. In these quantities the universal power-law emerges clearly, especially if one focuses on energy current and its fractionalization into a right- and left- moving components. In particular, we show that the presence of a transient in the energy fractionalization ratio is a direct hallmark of the quench-induced relaxation. Within the setup we have considered, time-dependent transport properties are thus promoted to useful and promising tools to access the mechanisms at the base of the out-of- equilibrium dynamics following quantum quench.

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Journal of Physics Conference Series•Mar 1, 2018•0 citations
The study of the relaxation process that follows a quantum quench in 1D systems still represents an open research field. Here we consider a sudden change of the interparticle interaction and we identify a peculiar correlator of the system whose behavior is directly and deeply affected by the quench-induced dynamics. Interestingly, it features a universal power-law decay in time. Unfortunately, such a universal decay, although present, turns out to be subleading in intrinsic properties of the system such as the non- equilibrium spectral function. We thus consider a tunnel coupling of the system with a biased tip in order to be able to study also transport properties, namely the charge and energy current flowing from the tip to the system after the quench. In these quantities the universal power-law emerges clearly, especially if one focuses on energy current and its fractionalization into a right- and left- moving components. In particular, we show that the presence of a transient in the energy fractionalization ratio is a direct hallmark of the quench-induced relaxation. Within the setup we have considered, time-dependent transport properties are thus promoted to useful and promising tools to access the mechanisms at the base of the out-of- equilibrium dynamics following quantum quench.
We investigate the time evolution towards the asymptotic steady state of a one-dimensional interacting system after a quantum quench. We show that at finite times the latter induces entanglement between right- and left-moving density excitations, encoded in their cross-correlators, which vanishes in the long-time limit. This behavior results in a universal time decay $\ensuremath{\propto}{t}^{\ensuremath{-}2}$ of the system spectral properties, in addition to nonuniversal power-law contributions typical of Luttinger liquids. Importantly, we argue that the presence of quench-induced entanglement clearly emerges in transport properties, such as charge and energy currents injected in the system from a biased probe and determines their long-time dynamics. In particular, the energy fractionalization phenomenon turns out to be a promising platform to observe the universal power-law decay $\ensuremath{\propto}{t}^{\ensuremath{-}2}$ induced by entanglement and represents a novel way to study the corresponding relaxation mechanism.
It has been shown that a quantum quench of interactions in a one-dimensional fermion system at zero temperature induces a universal power law proportional to t^{-2} t − 2 in its long-time dynamics. In this paper we demonstrate that this behaviour is robust even in the presence of thermal effects. The system is initially prepared in a thermal state, then at a given time the bath is disconnected and the interaction strength is suddenly quenched. The corresponding effects on the long times dynamics of the non-equilibrium fermionic spectral function are considered. We show that the non-universal power laws, present at zero temperature, acquire an exponential decay due to thermal effects and are washed out at long times, while the universal behaviour proportional to t^{-2} t − 2 is always present. To verify our findings, we argue that these features are also visible in transport properties at finite temperature. The long-time dynamics of the current injected from a biased probe exhibits the same universal power law relaxation, in sharp contrast with the non-quenched case which features a fast exponential decay of the current towards its steady value, and thus represents a fingerprint of quench-induced dynamics. Finally, we show that a proper tuning of the probe temperature, compared to that of the one-dimensional channel, can enhance the visibility of the universal power-law behaviour.
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.
We study the universal dynamical relaxation behaviors of a quantum XY chain following a quench, paying special attention to the case in which the initial state is a critical ground state, or the postquenched Hamiltonian is at a critical point of equilibrium quantum phase transition, or both of them are critical. In such a ``critical quench,'' we find very interesting real-time dynamical scaling behaviors and we find crossover phenomena between them. For a quench from a noncritical point to a critical point, we find that, compared to the noncritical quench, the universal power-law scaling behavior does not change; however, there may be a crossover between the exponential decaying behavior and the power-law scaling. For a quench from a critical point to a noncritical point, the power-law scaling behaviors ${t}^{\ensuremath{-}3/2}$ and ${t}^{\ensuremath{-}3/4}$ in the noncritical quenches may be changed to ${t}^{\ensuremath{-}1}$ and ${t}^{\ensuremath{-}1/2}$, respectively. If the prequenched Hamiltonian is set to be a point that is close to but not exactly at a critical point, we find interesting crossover phenomena between different power-law scaling behaviors. We also study the quench from the vicinity of a multicritical point, we find crossover behaviors that are induced by a different mechanism, and we find another crossover exponent. All the results are related to the gap-closing properties of the energy spectrum of the critical points.
Charge and energy fractionalization are among the most intriguing features of interacting one-dimensional fermion systems. In this work we determine how these phenomena are modified in the presence of an interaction quench. Charge and energy are injected into the system suddenly after the quench, by means of tunneling processes with a noninteracting one-dimensional probe. Here, we demonstrate that the system settles to a steady state in which the charge fractionalization ratio is unaffected by the prequenched parameters. On the contrary, due to the postquench nonequilibrium spectral function, the energy partitioning ratio is strongly modified, reaching values larger than 1. This is a peculiar feature of the nonequilibrium dynamics of the quench process and it is in sharp contrast with the nonquenched case, where the ratio is bounded by 1.
The spectral density of an interaction-quenched one-dimensional system is investigated. Both direct and inverse quench protocols are considered and it is found that the former leads to stronger effects on the spectral density with respect to the latter. Such asymmetry is directly reflected on transport properties of the system, namely the charge and energy current flowing to the system from a tunnel coupled biased probe. In particular, the injection of particles from the probe to the right-moving channel of the system is considered. The resulting fractionalization phenomena are strongly affected by the quench protocol and display asymmetries in the case of direct and inverse quench. Transport properties therefore emerge as natural probes for the observation of this quench-induced behavior.