Effects of the interplay between initial state and Hamiltonian on the thermalization of isolated quantum many-body systems

Abstract

We explore the role of the initial state on the onset of thermalization in isolated quantum many-body systems after a quench. The initial state is an eigenstate of an initial HamiltonianĤI and it evolves according to a different final HamiltonianĤF . If the initial state has a chaotic structure with respect toĤF , i.e., if it fills the energy shell ergodically, thermalization is certain to occur. This happens whenĤI is a full random matrix, because its states projected ontoĤF are fully delocalized. The results for the observables then agree with those obtained with thermal states at infinite temperature. However, finite real systems with few-body interactions, as the ones considered here, are deprived of fully extended eigenstates, even when described by a nonintegrable Hamiltonian. We examine how the initial state delocalizes as it gets closer to the middle of the spectrum ofĤF , causing the observables to approach thermal averages, be the models integrable or chaotic. Our numerical studies are based on initial states with energies that cover the entire lower half of the spectrum of one-dimensional Heisenberg spin-1/2 systems.

Local quenches with global effects in interacting quantum systems

“…The results reinforce the equivalence between the two models for the chosen values of d F and λ F . They also corroborate the dependence on temperature in the studies of thermalization [89,90].…”

“…[90], we studied quenches to the NNN model in the limit of strong perturbation, where the energy distribution of the initial state is Gaussian and therefore already approximately thermal, even before the quench. In such an extreme scenario, it was difficult to clearly discern improvements with T and L. Here, where the initial state is Breit-Wigner, these improvements are more visible.…”

Quantum chaos and thermalization in isolated systems of interacting particles

“…(7.1) is strictly dependent on the following parameters: the width of the strength function in connection with that of the energy shell and the microcanonical energy window. They also make evident that the viability of thermalization depends on the chosen initial state [262,263,264,51] (specifically, close to the edges of the energy band this approach might be not valid). Conventional thermalization is therefore not expected to occur for initial states whose widths of strength functions are smaller than the energy shell.…”

“…The analysis of how the energy of the initial state affects the viability of conventional thermalization was performed in [262,263,264,51]. In particular, it has been shown that thermalization may happen even in quenches where the final Hamiltonian is integrable provided the initial state spans over chaotic-like states of the total Hamiltonian.…”

Interaction quenches in the two-dimensional fermionic Hubbard model

“…The other dimensionality allowing for wellcontrolled studies is ∞D where dynamical mean-field theory becomes exact [19][20][21] and Gutzwiller approaches are well justified [22]. Exact diagonalization is completely flexible concerning dimensionality, but it is restricted to small systems [23,24].…”