Quantum Quench in the Transverse Field Ising Chain II: Stationary State Properties

We study the nonequilibrium time evolution of the spin-1/2 anisotropic Heisenberg (XXZ) spin chain, with a choice of dimer product and Neel states as initial states. We investigate numerically various short-ranged spin correlators in the long-time limit and find that they deviate significantly from predictions based on the generalized Gibbs ensemble (GGE) hypotheses. By computing the asymptotic spin correlators within the recently proposed quench-action formalism [Phys. Rev. ...

We consider the time evolution after quantum quenches in the spin-1/2 Heisenberg XXZ quantum spin chain with Ising-like anisotropy. The time evolution of short-distance spin-spin correlation functions is studied by numerical tensor network techniques for a variety of initial states, including N\'eel and Majumdar-Ghosh states and the ground state of the XXZ chain at large values of the anisotropy. The various correlators appear to approach stationary values, which are found to...

We present a quantitative semi-classical theory for the non-equilibrium dynamics of transverse Ising chains after quantum quenches, in particular sudden changes of the transverse field strength. We obtain accurate predictions for the quench dependent relaxation times and correlation lengths, and also about the recurrence times and quasiperiodicity of time dependent correlations in finite systems with open or periodic boundary conditions. We compare the quantiative predictions...

In this PhD thesis we investigate some properties of one-dimensional quantum systems, focusing on two important aspects of integrable models: Their entanglement properties at equilibrium and their dynamical correlators after a quantum quench. The first part of the thesis will therefore be devoted to the study of the entanglement entropy in one-dimensional integrable systems, with a special focus on the XYZ spin-1/2 chain, which, in addition to being integrable, is also an int...

The spin-1/2 quantum Ising chain in a transverse random magnetic field is studied by means of the density-matrix renormalization group. The system evolves from an ordered to a paramagnetic state as the amplitude of the random field is increased. The dependence of the magnetization on a uniform magnetic field in the z direction and the spontaneous magnetization as a function of the amplitude of the transverse random magnetic field are determined. The behavior of the spin-spin ...

We consider the non-stationary quantum relaxation of the Ising spin chain in a transverse field of strength h. Starting from a homogeneously magnetized initial state the system approaches a stationary state by a process possessing quasi long range correlations in time and space, independent of the value of $h$. In particular the system exhibits aging (or lack of time translational invariance on intermediate time scales) although no indications of coarsening are present.

We study the nonequilibrium dynamics of the Quantum Ising Model following an abrupt quench of the transverse field. We focus on the on-site autocorrelation function of the order parameter, and extract the phase coherence time $\tau^{\phi}_Q$ from its asymptotic behavior. We show that the initial state determines $\tau^{\phi}_Q$ only through an effective temperature set by its energy and the final Hamiltonian. Moreover, we observe that the dependence of $\tau^{\phi}_Q$ on the ...

The theory of dynamical quantum phase transitions represents an attempt to extend the concept of phase transitions to the far from equilibrium regime. While there are many formal analogies to conventional transitions, it is a major question to which extent it is possible to formulate a nonequilibrium counterpart to a Landau-Ginzburg theory. In this work we take a first step in this direction by constructing an effective free energy for continuous dynamical quantum phase trans...

A phase transition indicates a sudden change in the properties of a large system. For temperature-driven phase transitions this is related to non-analytic behavior of the free energy density at the critical temperature: The knowledge of the free energy density in one phase is insufficient to predict the properties of the other phase. In this paper we show that a close analogue of this behavior can occur in the real time evolution of quantum systems, namely non-analytic behavi...

We study the non-equilibrium time evolution of the average transverse magnetisation and end-to-end correlation functions of the random Ising quantum chain. Starting with fully magnetised states, either in the $x$ or $z$ direction, we compute numerically the average quantities. They show similar behaviour to the homogeneous chain, that is an algebraic decay in time toward a stationary state. During the time evolution, the spatial correlations, measured from one end to the othe...