We study one-dimensional lattices of interacting spins-1/2 and show that the effects of quenching the amplitude of a local magnetic field applied to a single site of the lattice can be comparable to the effects of a global perturbation applied instantaneously to the entire system. Both quenches take the system to the chaotic domain, the energy distribution of the initial states approaches a Breit-Wigner shape, the fidelity (Loschmidt echo) decays exponentially, and thermalization becomes viable.

We study numerically and analytically isolated interacting quantum systems that are taken out of equilibrium instantaneously (quenched). The probability of finding the initial state in time, the so-called fidelity, decays fastest for systems described by full random matrices, where simultaneous many-body interactions are implied. In the realm of realistic systems with two-body interactions, the dynamics is slower and depends on the interplay between the initial state and the Hamiltonian characterizing the system. The fastest fidelity decay in this case is Gaussian and can persist until saturation. A simple general picture, in which the fidelity plays a central role, is also achieved for the short-time dynamics of few-body observables. It holds for initial states that are eigenstates of the observables. We also discuss the need to reassess analytical expressions that were previously proposed to describe the evolution of the Shannon entropy. Our analyses are mainly developed for initial states that can be prepared in experiments with cold atoms in optical lattices. INTRODUCTIONDespite the ubiquity of many-body quantum systems out of equilibrium, they are much less understood than quantum systems in equilibrium. To advance our understanding and to construct a general picture, it is necessary to identify the elements that lead to similar dynamics. Determining how fast these systems evolve in time [1-5] is also essential for the development of algorithms for quantum optimal control [6]. In these two contexts, the unitary evolution of isolated many-body quantum systems is of particular interest due, in part, to the connection with current experiments in optical lattices [7][8][9][10][11][12][13][14][15][16][17]. The latter are quasi-isolated systems, where coherent evolutions can be studied for very long times.The evolution of an isolated system can be initiated by changing instantaneously the parameters of a certain initial Hamiltonian which is brought into a new final Hamiltonian. This abrupt perturbation is referred to as a quench. The system starts off in an eigenstate of the initial Hamiltonian. The fidelity (return probability) [18,19], which is defined as the overlap between the initial state and its evolved counterpart, is a way to characterize the system evolution. This quantity is related to the Loschmidt echo. It is also analogous to the characteristic function of the probability distribution of work [20][21][22][23] and is therefore likely to find applications in quantum thermodynamics, particularly in studies related with the quantification of the work done to take quantum systems out of equilibrium. The fidelity decays exponentially when the final Hamiltonian is chaotic [24][25][26][27][28][29][30][31][32]. In fact, this behavior is expected to hold even in integrable Hamiltonians provided the initial state be sufficiently delocalized in the energy eigenbasis [33][34][35].Here, we extend the results obtained in Ref. [36] and show that the fidelity can have a faster than exponential behavior. The fidelity ...

The isolated one-dimensional Heisenberg model with static random magnetic fields has become paradigmatic for the analysis of many-body localization. Here, we study the dynamics of this system initially prepared in a highly-excited nonstationary state. Our focus is on the probability for finding the initial state later in time, the so-called survival probability. Two distinct behaviors are identified before equilibration. At short times, the decay is very fast and equivalent to that of clean systems. It subsequently slows down and develops a power-law behavior with an exponent that coincides with the multifractal dimension of the eigenstates.

This work supports the existence of extended nonergodic states in the intermediate region between the chaotic (thermal) and the many-body localized phases. These states are identified through an extensive analysis of static and dynamical properties of a finite one-dimensional system with onsite random disorder. The long-time dynamics is particularly sensitive to changes in the spectrum and in the structures of the eigenstates. The study of the evolution of the survival probability, Shannon information entropy, and von Neumann entanglement entropy enables the distinction between the chaotic and the intermediate region.Comment: 10 pages, 7 figures, Contribution to the Special Issue "Many-Body Localization" in Annalen der Physi