Generalized Thermalization in an Integrable Lattice System (original) (raw)
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Relaxation and Thermalization of Isolated Many-Body Quantum Systems
We provide an overview of our numerical and analytical studies of isolated interacting quantum systems that are taken out of equilibrium instantaneously (quenched). We describe the relaxation process to a new equilibrium and obtain lower bounds for the relaxation time of full random matrices and realistic systems with two-body interactions. We show that the size of the time fluctuations after relaxation decays exponentially with system size for systems without too many degeneracies. We also discuss the conditions for thermalization and demonstrate that it can happen after local and global quenches in space. The analyses are developed for systems, initial states, and few-body observables accessible to experiments with optical lattices.
Generalized thermalization for integrable system under quantum quench
2016
We investigate equilibration and generalized thermalization of the quantum Harmonic chain under local quantum quench. The quench action we consider is connecting two disjoint harmonic chains of different sizes and the system jumps between two integrable settings. We verify the validity of the Generalized Gibbs Ensemble description for this infinite dimensional Hilbert space system and also identify equilibration between the subsystems as in classical systems. Using Bogoliubov transformations, we show that the eigenstates of the system prior to the quench evolve towards the Gibbs Generalized Ensemble description. Eigenstates that are more delocalized (in the sense of inverse participation ratio) prior to the quench, tend to equilibrate more rapidly. Further, through the phase space properties of a Generalized Gibbs Ensemble and the strength of stimulated emission, we identify the necessary criterion on the initial states for such relaxation at late times and also find out the states ...
Quantum quenches, thermalization, and many-body localization
Physical Review B, 2011
We discuss how thermalization following a quantum quench in a strongly correlated quantum system is intimately connected to many-body localization in the space of quasi-particles. We test our picture in the anisotropic Heisenberg spin chain with an integrability-breaking term. We first quantify the deviations from integrability by analyzing the level spacing statistics and the characteristics of the system eigenstates. We then focus on thermalization by studying the dynamics after a sudden quench of the anisotropy parameter. PACS numbers: 75.10.Jm, 72.15.Rn, 05.45.Mt The understanding of ergodicity and thermalization in quantum systems is one of the most intriguing problems in quantum physics. Starting with the 1929 paper of von Neumann [1], various attempts have been made towards the characterization of ergodic behavior in quantum systems , and the establishment of a link with the notion of quantum chaos . Theoretical interest in these issues resurfaced periodically until very recently, when an experimental study of the non-equilibrium dynamics of a quasi-one-dimensional condensate clearly demonstrated the lack of thermalization/ergodicity in a quantum many-body system . The attribution of this observation to quantum integrability generated a lot of interest on its connections with ergodicity and thermalization in strongly-correlated quantum systems .
Absence of Thermalization in Nonintegrable Systems
2010
We establish a link between unitary relaxation dynamics after a quench in closed many-body systems and the entanglement in the energy eigenbasis. We find that even if reduced states equilibrate, they can have memory on the initial conditions even in certain models that are far from integrable. We show that in such situations the equilibrium states are still described by a maximum entropy or generalized Gibbs ensemble, regardless of whether a model is integrable or not, thereby contributing to a recent debate. In addition, we discuss individual aspects of the thermalization process, comment on the role of Anderson localization, and collect and compare different notions of integrability.
Effective Thermal Dynamics Following a Quantum Quench in a Spin Chain
Physical Review Letters, 2009
We study the nonequilibrium dynamics of the Quantum Ising Model following an abrupt quench of the transverse field. We focus on the onsite autocorrelation function of the order parameter, and extract the phase coherence time τ ϕ Q from its asymptotic behavior. We show that the initial state determines τ ϕ Q only through an effective temperature set by its energy and the final Hamiltonian. Moreover, we observe that the dependence of τ ϕ Q on the effective temperature fairly agrees with that obtained in thermal equilibrium as a function of the equilibrium temperature.
Relaxation and thermalization after a quantum quench: Why localization is important
Physical Review B, 2013
We study the unitary dynamics and the thermalization properties of free-fermion-like Hamiltonians after a sudden quantum quench, extending the results of S. Ziraldo et al. [Phys. Rev. Lett. 109, 247205 (2012)]. With analytical and numerical arguments, we show that the existence of a stationary state and its description with a generalized Gibbs ensemble (GGE) depend crucially on the observable considered (local versus extensive) and on the localization properties of the final Hamiltonian. We present results on two one-dimensional (1D) models, the disordered 1D fermionic chain with long-range hopping and the disordered Ising/XY spin chain. We analytically prove that, while time averages of one-body operators are perfectly reproduced by GGE (even for finite-size systems, if time integrals are extended beyond revivals), time averages of many-body operators might show clear deviations from the GGE prediction when disorder-induced localization of the eigenstates is at play.
Physical Review A, 2014
Motivated by recent experiments, we study the relaxation dynamics and thermalization in the onedimensional Bose-Hubbard model induced by a global interaction quench. Specifically, we start from an initial state that has exactly one boson per site and is the ground state of a system with infinitely strong repulsive interactions at unit filling. Using exact diagonalization and the density matrix renormalization group method, we compute the time dependence of such observables as the multiple occupancy and the momentum distribution function. Typically, the relaxation to stationary values occurs over just a few tunneling times. The stationary values are identical to the so-called diagonal ensemble on the system sizes accessible to our numerical methods and we further observe that the micro-canonical ensemble describes the time averages of many observables reasonably well for small and intermediate interaction strength. The expectation values of observables in the canonical ensemble agree quantitatively with the time averages obtained from the quench at small interaction strengths, and qualitatively provide a good description even in parameter regimes where the microcanonical ensemble is not applicable due to finite-size effects. We discuss our numerical results in the framework of the eigenstate thermalization hypothesis. Moreover, we also observe that the diagonal and the canonical ensemble are practically identical for our initial conditions already on the level of their respective energy distributions for small interaction strengths. Finally, we discuss implications of our results for the interpretation of a recent sudden expansion experiment [Phys. Rev. Lett. 110, 205301 (2013)], in which the same interaction quench was realized.
Local emergence of thermal correlations in an isolated quantum many-body system
Nature Physics, 2013
Understanding the dynamics of isolated quantum manybody systems is a central open problem at the intersection between statistical physics and quantum physics. Despite important theoretical effort 1 , no generic framework exists yet to understand when and how an isolated quantum system relaxes to a steady state. Regarding the question of how, it has been conjectured 2,3 that equilibration must occur on a local scale in systems where correlations between distant points can establish only at a finite speed. Here, we provide the first experimental observation of this local equilibration hypothesis. In our experiment, we quench a one-dimensional Bose gas by coherently splitting it into two parts. By monitoring the phase coherence between the two parts we observe that the thermal correlations of a prethermalized state 4,5 emerge locally in their final form and propagate through the system in a light-cone-like evolution. Our results underline the close link between the propagation of correlations 2,3,6,7 and relaxation processes in quantum many-body systems.