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arXiv:1609.07387 · Physical review. B./Physical review. B

Spreading of correlations in a quenched repulsive and attractive one-dimensional integrable system

Luca Barbiero, Luca Dell’Anna

Published Aug 8, 2017• 4 citations
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Abstract

We study the real-time evolution of the correlation functions in a globally quenched interacting one-dimensional lattice system by means of time-adaptive density matrix renormalization group. We find a clear light-cone behavior quenching the repulsive interaction from the gapped density wave regime. The spreading velocity increases with the final values of the interaction and then saturates at a certain finite value. In the case of a Luttinger liquid phase as the initial state, for strong repulsive interaction quenches, a more complex dynamics occurs as a result of bound state formations. From the other side in the attractive regime, depending on where connected correlation functions are measured, one can observe a delay in the starting time evolution and a coexistence of ballistic and localized signals.

DOI
10.1103/physrevb.96.064303

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We study the real-time evolution of the correlation functions in a globally quenched interacting one-dimensional lattice system by means of time-adaptive density matrix renormalization group. We find a clear light-cone behavior quenching the repulsive interaction from the gapped density wave regime. The spreading velocity increases with the final values of the interaction and then saturates at a certain finite value. In the case of a Luttinger liquid phase as the initial state, for strong repulsive interaction quenches, a more complex dynamics occurs as a result of bound state formations. From the other side in the attractive regime, depending on where connected correlation functions are measured, one can observe a delay in the starting time evolution and a coexistence of ballistic and localized signals.
Using the adaptive time-dependent density-matrix renormalization group, we study the time evolution of density correlations of interacting spinless fermions on a one-dimensional lattice after a sudden change in the interaction strength. Over a broad range of model parameters, the correlation function exhibits a characteristic light-cone-like time evolution representative of a ballistic transport of information. Such behavior is observed both when quenching an insulator into the metallic region and also when quenching within the insulating region. However, when a metallic state beyond the quantum critical point is quenched deep into the insulating regime, no indication for ballistic transport is observed. Instead, stable domain walls in the density correlations emerge during the time evolution, consistent with the predictions of the Kibble-Zurek mechanism.
We provide evidence that the relaxation dynamics of one-dimensional, metallic Fermi systems resulting out of an abrupt amplitude change of the two-particle interaction has aspects which are universal in the Luttinger liquid sense: the leading long-time behavior of certain observables is described by universal functions of the equilibrium Luttinger liquid parameter and the renormalized velocity. We analytically derive those functions for the Tomonaga-Luttinger model and verify our hypothesis of universality by considering spinless lattice fermions within the framework of the density-matrix renormalization group.
We investigate the spread of correlations in a one-dimensional lattice system with high on-site energy disorder and long-range couplings with a power-law dependence on the distance ($\ensuremath{\propto}{r}^{\ensuremath{-}\ensuremath{\mu}}$). The increase in correlation between the initially quenched node and a given node exhibits three phases: quadratic in time, linear in time, and saturation. No further evolution is observed in the long time regime. We find an approximate solution of the model valid in the limit of strong disorder and reproduce the results of numerical simulations with analytical formulas. We also find the time needed to reach a given correlation value as a measure of the propagation speed. Because of the triple-phase evolution of the correlation function, the propagation changes its time dependence. In the particular case of $\ensuremath{\mu}=1$, the propagation starts as a ballistic motion and then, at a certain crossover time, turns into standard diffusion.
Using a Luttinger liquid theory we investigate the time evolution of the particle density of a one-dimensional spinful fermionic system with open boundaries and subject to a finite-duration quench of the inter-particle interaction. Taking into account also the turning on of an umklapp perturbation to the system Hamiltonian as a result of the quench, we study the possible formation of a Wigner molecule inside the system, focusing in particular on the sudden and adiabatic regimes. We show that the creation of this correlated state is essentially due to the propagation of "light-cone" perturbations through system which arise after both switching on and switching off the quenching protocol and that its behavior strongly depends on the quench duration.
Using the adaptive time-dependent density-matrix renormalization group method, we study the time evolution of strongly correlated spinless fermions on a one-dimensional lattice after a sudden change of the interaction strength. For certain parameter values, two different initial states (e.g., metallic and insulating) lead to observables which become indistinguishable after relaxation. We find that the resulting quasistationary state is nonthermal. This result holds for both integrable and nonintegrable variants of the system.
We investigate the collapse and revival of the initial state of a system of spinless fermions on a one‐dimensional lattice with nearest‐neighbor Coulomb repulsion V and nearest‐neighbor hopping t at half filling which we push out of equilibrium. Starting from a Luttinger liquid phase, we suddenly increase the interaction to a value associated with an insulating ground state. Using a variant of the time‐dependent density matrix renormalization group method (DMRG) that approximates the time‐evolution operator within a Krylov subspace, we calculate the full time evolution of quantities like the momentum distribution 〈nk〉 and the local density 〈ni〉. In the atomic limit, t = 0, the density and the density‐density correlation function are time‐independent, while 〈nk〉 changes with time, showing that in out‐of‐equilibrium situations density‐density correlations and one‐particle propagators are no longer connected by a single anomalous dimension as in the equilibrium case. Since in this limit the initial state is reobtained after Trevival = 2π/(V/t), the collapse and revival of the initial Luttinger liquid equilibrium state is discussed. Preliminary results providing insight into the behavior in the thermodynamic limit for various parameter values with finite hopping amplitude t ≠ 0 are presented.