Quenched dynamics in interacting one-dimensional systems: Appearance of current-carrying steady states from initial domain wall density profiles

Lancaster, Jarrett L.; Gull, Emanuel; Mitra, Aditi

doi:10.1103/physrevb.82.235124

Cited by 23 publications

(28 citation statements)

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“…As a result, the transverse spin correlation function in these simple models were found to reach a nonequilibrium steady state which showed spatial oscillations at a wavelength inversely related to the magnitude of the current [26]. As back-scattering interactions were added, the current was found to decrease, and consequently, the wavelength of the oscillations in the transverse spin correlation function was found to increase [27]. These results are further explored here taking into account both integrable and nonintegrable systems.…”

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confidence: 76%

“…In the context of thermalization, the dynamics of a sharp domain wall in the * Electronic address: lsantos2@yu.edu † Electronic address: aditi.mitra@nyu.edu gapped phase of the XXZ chain was studied using Algebraic Bethe Ansatz in [24]. The evolution of a domain wall state was investigated analytically in [25] and [26] for the XX model and numerically employing the truncated Wigner approximation for the quantum sine-Gordon model [27]. The domain wall in the XX model and the Luttinger liquid was found to spread out ballistically into a current carrying steady state [26,27].…”

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confidence: 99%

“…The evolution of a domain wall state was investigated analytically in [25] and [26] for the XX model and numerically employing the truncated Wigner approximation for the quantum sine-Gordon model [27]. The domain wall in the XX model and the Luttinger liquid was found to spread out ballistically into a current carrying steady state [26,27]. In a spin-chain, current flow implies a rotation in space of the transverse component of the spins.…”

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Domain wall dynamics in integrable and chaotic spin-1/2 chains

Santos

Mitra

2011

Phys. Rev. E

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We study the time evolution of correlation functions, spin current, and local magnetization in an isolated spin-1/2 chain initially prepared in a sharp domain wall state. The results are compared with the level of spatial delocalization of the eigenstates of the system which is measured using the inverse participation ratio. Both integrable and non-integrable regimes are considered. Nonintegrability is introduced to the integrable Hamiltonian with nearest neighbor couplings by adding a single site impurity field or by adding next-nearest-neighbor couplings. A monotonic correspondence between the enhancement of the level of delocalization, spin current and magnetization dynamics occurs in the integrable domain. This correspondence is however lost for chaotic models with weak Ising interactions.

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Domain wall dynamics in integrable and chaotic spin-1/2 chains

Santos

Mitra

2011

Phys. Rev. E

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“…[27][28][29][30][31][32][33][34][35][36] Prior art on Luttinger liquid, sine-Gordon, and XXZ chain quenches includes that of Refs. 17,19,21,[29][30][31][32][33][34][37][38][39]. Wavepackets have been previously employed in the study of excitations induced by a local quench, [40][41][42] in which the Hamiltonian deformation is restricted to a spatial subregion of the larger system.…”

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confidence: 99%

Quantum quench spectroscopy of a Luttinger liquid: Ultrarelativistic density wave dynamics due to fractionalization in anXXZchain

et al. 2011

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We compute the dynamics of localized excitations produced by a quantum quench in the spin 1/2 XXZ chain. Using numerics combining the density matrix renormalization group and exact time evolution, as well as analytical arguments, we show that fractionalization due to interactions in the pre-quench state gives rise to "ultrarelativistic" density waves that travel at the maximum band velocity. The system is initially prepared in the ground state of the chain within the gapless XY phase, which admits a Luttinger liquid (LL) description at low energies and long wavelengths. The Hamiltonian is then suddenly quenched to a band insulator, after which the chain evolves unitarily. Through the gapped dispersion of the insulator spectrum, the post-quench dynamics serve as a "velocity microscope," revealing initial state particle correlations via space time density propagation. We show that the ultrarelativistic wave production is tied to the particular way in which fractionalization evades Pauli-blocking in the zero-temperature initial LL state.

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“…However, not much attention has been devoted to the study of quantum quenches between gapless and gapped states. A notable exception is represented by quantum quenches from a Luttinger liquid to a sine-Gordon model [52][53][54][55][56][57][58][59][60][61] and quantum time mirrors 62 . However, the characterization of the main features of gapless-to-gapped quantum quenches is still lacking.…”

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Nonmonotonic response and light-cone freezing in fermionic systems under quantum quenches from gapless to gapped or partially gapped states

et al. 2018

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The properties of prototypical examples of one-dimensional fermionic systems undergoing a sudden quantum quench from a gapless state to a (partially) gapped state are analyzed. By means of a Generalized Gibbs Ensemble analysis or by numerical solutions in the interacting cases, we observe an anomalous, non-monotonic response of steady state correlation functions as a function of the strength of the mechanism opening the gap. In order to interpret this result, we calculate the full dynamical evolution of these correlation functions, which shows a freezing of the propagation of the quench information (light cone) for large quenches. We argue that this freezing is responsible for the non-monotonous behaviour of observables. In continuum non-interacting models, this freezing can be traced back to a Klein-Gordon equation in the presence of a source term. We conclude by arguing in favour of the robustness of the phenomenon in the cases of non-sudden quenches and higher dimensionality.PACS numbers: 67.85. Lm, 05.70.Ln, 71.70.Ej, 05.30.Fk Non-equilibrium quantum physics is at the heart of most relevant applications of solid state physics, such as transistors and lasers [1][2][3] . More fundamentally, one of the main difficulties in studying many-body non-equilibrium quantum physics is represented by the unavoidable interactions that any quantum system has with its surroundings. This coupling is difficult to control and causes an effectively non-unitary evolution even on short time scales 4 . The recent advent of cold atom physics 5 allowed not only to access quantum systems characterized by weak coupling to the environment, but also to engineer Hamiltonians which show non-ergodic behavior 6,7 : the so called integrable systems 8 . Moreover, in the context of cold atom physics, it is possible to manipulate the parameters of the Hamiltonian in a time dependent and controllable fashion 7,9-12 . The combination of these three ingredients gave rise to a renewed interest in the physics of quantum quenches [13][14][15][16][17] , which led to the birth of a new thermodynamic ensemble, the Generalized Gibbs Ensemble (GGE) 1,[18][19][20][21]23 . Quantum quenches have been studied in a wide range of systems with the property that a change in a parameter of the Hamiltonian deeply affects the physical properties of the system itself. Interaction quenches in Luttinger liquids [24][25][26][27][28][29][30][31][32][33][34][35][36] and magnetic field quenches in the one-dimensional (1D) Ising model [37][38][39][40][41][42][43][44][45][46][47] are prominent examples in this direction. Furthermore, at the level of free fermions, quantum quenches between gapped phases characterized by different Chern numbers have also been studied [48][49][50][51] . However, not much attention has been devoted to the study of quantum quenches between gapless and gapped states. A notable exception is represented by quantum quenches from a Luttinger liquid to a sine-Gordon model [52][53][54][55][56][57][58][59][60][61] and quantum time mirrors 62 . However...

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Quenched dynamics in interacting one-dimensional systems: Appearance of current-carrying steady states from initial domain wall density profiles

Cited by 23 publications

References 25 publications

Domain wall dynamics in integrable and chaotic spin-1/2 chains

Domain wall dynamics in integrable and chaotic spin-1/2 chains

Quantum quench spectroscopy of a Luttinger liquid: Ultrarelativistic density wave dynamics due to fractionalization in anXXZchain

Nonmonotonic response and light-cone freezing in fermionic systems under quantum quenches from gapless to gapped or partially gapped states

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