We numerically investigate the relaxation dynamics in an isolated quantum system of interacting bosons trapped in a double-well potential after an integrability breaking quench. Using the statistics of the spectrum, we identify the postquench Hamiltonian as nonchaotic and close to integrability over a wide range of interaction parameters. We demonstrate that the system exhibits thermalization in the context of the eigenstate thermalization hypothesis (ETH). We also explore the possibility of an initial state to delocalize with respect to the eigenstates of the postquench Hamiltonian even for energies away from the middle of the spectrum. We observe distinct regimes of equilibration process depending on the initial energy. For low energies, the system rapidly relaxes in a single step to a thermal state. As the energy increases towards the middle of the spectrum, the relaxation dynamics exhibits prethermalization and the lifetime of the metastable states grows. Time evolution of the occupation numbers and the von Neumann entropy in the mode-partitioned system underpins the analyses of the relaxation dynamics.
We investigate the crossover of the entanglement entropy toward its thermal value in nearly integrable systems. We employ equations-of-motion techniques to study the entanglement dynamics in a lattice model of weakly interacting spinless fermions after a quantum quench. For weak enough interactions we observe a two-step relaxation of the entanglement entropies of finite subsystems. Initially, the entropies follow a nearly integrable evolution, approaching the value predicted by the generalized Gibbs ensemble (GGE) of the unperturbed model. Then, they start a slow drift toward the thermal stationary value described by a standard Gibbs ensemble (GE). While the initial relaxation to the GGE is independent of the interaction, the slow drift from GGE to GE values happens on timescales proportional to the inverse interaction squared. For asymptotically large times and subsystem sizes the dynamics of the entropies can be predicted using a modified quasiparticle picture that keeps track of the evolution of the fermionic occupations caused by the integrability breaking. This picture gives a quantitative description of the results as long as the integrability-breaking timescale is much larger than the one associated with the (quasi)saturation to the GGE. In the opposite limit, the quasiparticle picture still provides the correct late-time behavior, but it underestimates the initial slope of the entanglement entropy.
We study the dynamics and thermalization of strongly correlated fermions in finite one-dimensional lattices after a quantum quench. Our calculations are performed using exact diagonalization. We focus on one- and two-body observables such as the momentum distribution function
[n(k)] and the density-density structure factor
[N(k)], respectively, and study the effects of approaching an integrable point. We show that while the relaxation dynamics and thermalization of
N(k) for fermions is very similar to the one of hardcore bosons, the behavior of
n(k) is distinctively different. The latter observable exhibits a slower relaxation dynamics in fermionic systems. We identify the origin of this behavior, which is related to the off-diagonal matrix elements of
n(k) in the basis of the eigenstates of the Hamiltonian. More generally, we find that thermalization occurs far away from integrability and that it breaks down as one approaches the integrable point.
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 study the relaxation dynamics of interacting one-dimensional fermions with band curvature after a weak quench in the interaction parameter at zero temperature. Our model lies within the class of interacting Luttinger liquids, where the harmonic Luttinger theory is extended by a weak-integrability-breaking phonon scattering term. In order to solve for the nonequilibrium time evolution, we use quantum kinetic equations exploiting the resonant but subleading character of the phonon interaction term. The interplay between phonon scattering and the quadratic Luttinger theory leads to the emergence of three distinct spatiotemporal regimes for the fermionic real-space correlation function. It features the crossover from a prequench to a prethermal state, finally evolving towards a thermal state on increasing length and time scales. The characteristic algebraically decaying real-space correlations in the prethermalized regime become modulated by an amplitude that is decaying in time according to a stretched exponential as an effect of the interactions. The asymptotic thermalization dynamics is governed by energy transport over large distances from the thermalized to the nonthermalized regions via macroscopic, dynamical slow modes. This is revealed in an algebraic decay of the system's effective temperature. The numerical value of the associated exponent agrees with the dynamical critical exponent of the Kardar-Parisi-Zhang universality class. We also discuss a criterion for the applicability of this theory away from the integrable limit of noninteracting fermions.
We study the out-of-equilibrium dynamics of one-dimensional quantum Ising-like systems, arising from sudden quenches of the Hamiltonian parameter
g driving quantum transitions between disordered and ordered phases. In particular, we consider quenches to values of
g around the critical value
gc, and mainly address the question whether, and how, the quantum transition leaves traces in the evolution of the transverse and longitudinal magnetizations during such a deep out-of-equilibrium dynamics. We shed light on the emergence of singularities in the thermodynamic infinite-size limit, likely related to the integrability of the model. Finite systems in periodic and open boundary conditions develop peculiar power-law finite-size scaling laws related to revival phenomena, but apparently unrelated to the quantum transition, because their main features are generally observed in quenches to generic values of
g. We also investigate the effects of dissipative interactions with an environment, modeled by a Lindblad equation with local decay and pumping dissipation operators within the quadratic fermionic model obtainable by a Jordan-Wigner mapping. Dissipation tends to suppress the main features of the unitary dynamics of closed systems. We finally address the effects of integrability breaking, due to further lattice interactions, such as in anisotropic next-to-nearest-neighbor Ising (ANNNI) models. We show that some qualitative features of the post-quench dynamics persist, in particular, the different behaviors when quenching to quantum ferromagnetic and paramagnetic phases, and the revival phenomena due to the finite size of the system.