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arXiv:1610.04492 · Physical review. B./Physical review. B

Nonequilibrium effects on charge and energy partitioning after an interaction quench

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

Published Feb 1, 2017• 15 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physrevb.95.085101

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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 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.
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.
We investigate the non-equilibrium dynamics of wave packets in a one-dimensional critical fermionic system and analyze the resulting partitioning of energy between emergent excitations. Starting from a Gaussian wave packet injected on top of the many-body ground state, we follow its real-time evolution using the time-dependent density-matrix renormalization group. We observe that interactions lead to fractionalization of the initial excitation into counter-propagating left- and right-moving modes, whose energies can be resolved in real space. To interpret these results, we employ Luttinger liquid theory, which allows us to derive analytical predictions for the energy carried by the emergent modes. We find good agreement between field-theoretical predictions and numerical simulations in the low-energy regime. In contrast to charge fractionalization, which is completely determined by the Luttinger liquid parameter, we show that energy partitioning is non-universal and depends on details of the injected wave packet, such as its width. Our results provide a real-space characterization of energy partitioning in one-dimensional systems and establish a quantitative comparison between non-equilibrium numerical simulations and the effective field-theory description.
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.
We study the nonequilibrium quench dynamics of a one-dimensional anyonic gas. We focus on the integrable anyonic Lieb-Liniger model and consider the quench from noninteracting to hard-core anyons. We study the dynamics of the local properties of the system. By means of integrability-based methods, we compute analytically the one-body density matrix and the density-density correlation function at all times after the quench and in particular at infinite time. Our results show that the system evolves from an initial state where the local momentum distribution function is nonsymmetric to a steady state where it becomes symmetric. Furthermore, while the initial momentum distribution functions (and the equilibrium ones) explicitly depend on the anyonic parameter, the final ones do not. This is reminiscent of the dynamical fermionization observed in the context of free expansions after release from a confining trap.
There are many ways to characterize quantum systems, for example, by measuring system-specific observables or probing their response to external perturbations. A complementary approach is based on quantum information measures. Independent of the microscopic details, it offers a universal perspective on quantum systems and enables a unified characterization of diverse quantum systems. Central, in this regard, is the determination of the quantum entanglement within a quantum system. Recently, in the interest of studying genuine nonequilibrium properties of a quantum system, the dynamics of the quantum entanglement have been established as a powerful approach to gain deep insights into the structure of quantum matter. In this Thesis, we investigate the entanglement dynamics in one-dimensional non-interacting fermionic chains following a quantum quench, i.e. after a sudden change of the system parameters. We propose a new and generic setting for the analysis of entanglement spreading in complex inhomogeneous systems, which we call a hybrid quench-probe setup. The key feature of this new approach is a separation between the quenched part of the system and a static probe region, where the quench induced entanglement spreading is measured. This separation allows a spatial and energy-resolved analysis of the entanglement dynamics. We demonstrate the capability of our protocol by identifying fractionally quantized entanglement jumps of log(2)/2 as a signature of fractionalized topological quasi-particles, such as isolated Majorana modes, that appear at the edges of an open-boundary Kitaev chain in the topological phase. In addition, we observe in this setup an interesting nonequilibrium effect: a static and a propagating contribution to the entanglement dynamics. To understand the origin of this effect, a local perspective on the entanglement structure is necessary. For this purpose, we employ the information lattice, which offers a local scale-resolved decomposition of the correlations present in a quantum state. In nonequilibrium systems with unitary dynamics, this framework enables a hydrodynamic description of the information flow through local densities and currents. Using the information lattice, we analyze three quantum quenches in one-dimensional fermionic systems and identify spatiotemporal features of the local information flow, such as information interfaces and long-range transport from topological edge modes. This analysis enables us to derive an analytical description of the nonequilibrium effect observed in the quenched Kitaev chain.