Quantum correlations in periodically driven spin chains: Revivals and steady-state properties (original) (raw)

Dynamics and steady state properties of entanglement in periodically driven Ising spin-chain

2017

We study the dynamics of microscopic quantum correlations, viz., bipartite entanglement and quantum discord, in Ising spin chain with periodically varying external magnetic field along the transverse direction. Depending upon system parameters, local quantum correlations in the evolved states of such systems may get saturated to non-zero values after sufficiently large number of driving cycles. Moreover, we investigate convergence of the local density matrices, from which the quantum correlations under study originate, towards the final steady-state density matrices as a function of driving cycles. We find that the geometric distance between the non-equilibrium and the steady-state reduced density matrices obey power-law scaling. The steady-state quantum correlations corresponding to various initial states in thermal equilibrium are studied as a function of drive time period of a square pulsed field. The steady-state quantum correlations are marked by presence of peaks in the freque...

Probing the Possibilities of Ergodicity in the 1D Spin-1/2 XY Chain with Quench Dynamics

Scientific Reports

Ergodicity sits at the heart of the connection between statistical mechanics and dynamics of a physical system. By fixing the initial state of the system into the ground state of the Hamiltonian at zero temperature and tuning a control parameter, we consider the occurrence of the ergodicity with quench dynamics in the one-dimensional (1D) spin-1/2 XY model in a transverse magnetic field. The ground-state phase diagram consists of two ferromagnetic and paramagnetic phases. It is known the magnetization in this spin system is non-ergodic. We set up two different experiments as we call them single and double quenches and test the dynamics of the magnetization along the Z-axis and the spinspin correlation function along the X-axis which are the order parameters of the zero-temperature phases. Our exact results reveal that for single quenches at zero-temperature, the ergodicity depends on the initial state and the order parameter. In single quenches for a given order parameter, ergodicity will be observed with an ergodic-region for quenches from another phase, non-correspond to the phase of the order parameter, into itself. In addition, a quench from a ground-state phase point corresponding to the order parameter into or very close to the quantum critical point, h c = 1.0, discloses an ergodic behavior. Otherwise, for all other single quenches, the system behaves non-ergodic. Interestingly on the other setup, a double quench on a cyclic path, ergodicity is completely broken for starting from the phase corresponding to the order parameter. Otherwise, it depends on the first quenched point, and the quench time T when the model spent before a second quench in the way back which gives an ability to controlling the ergodicity in the system. Therefore, and contrary to expectations, in the mentioned model the ergodicity can be observed with probing quench dynamics at zero-temperature. Our results provide further insight into the zero-temperature dynamical behavior of quantum systems and their connections to the ergodicity phenomenon. One of the most controversial topics is how the statistical mechanics behavior could emerge in quantum-mechanical systems evolving under unitary dynamics 1-12. Historically, von Neumann was the first one that worked on the topic. Instead of physical state (or wave function) of the system, he focused on macroscopic observables and introduced the quantum ergodic theorem. The quantum ergodic theorem says every initial wave function from a microcanonical energy shell evolves so that for most times, in the long run, the joint probability distribution of commuting macroscopic observables obtained from the unitarily time-evolved wave function is close to the microcanonical distribution of commuting observables. Study of quantum ergodicity in spin systems has been of interest for a long time. In 1970, for the first time, Barouch and coworkers 13 studied the dynamics of the magnetization of the anisotropic spin-1/2 XY chain. In fact they used a single quench at finite temperature where their initial and final states were thermal states. In addition, they did not probe all quenches. By a quench from the paramagnetic phase into itself they showed that the equilibrium is not reached at the final evolutionary time and then the magnetization is a non-ergodic observable. This non-ergodic behavior was later confirmed for the entanglement between the nearest neighbor pair spins of the evolved states 14. In addition to the 1D XY model, the non-ergodicity has been also studied in quantum chaos 15 , 1D XXZ model to show ergodicity breaking that can create a many-body localization 16 and its extended 17 , 1D system of spinless and interacting fermions with a disordered potential 18 , the anisotropic Dicke model 19 , and in a small quantum system consisting of three superconducting qubits by measuring the evolution of the entanglement entropy 20 .

Ergodicity from Nonergodicity in Quantum Correlations of Low-dimensional Spin Systems

2011

Correlations between the parts of a many-body system, and its time dynamics, lie at the heart of sciences, and they can be classical as well as quantum. Quantum correlations are traditionally viewed as constituted out of classical correlations and magnetizations. While that of course remains so, we show that quantum correlations can have statistical mechanical properties like ergodicity, which is not inherited from the corresponding classical correlations and magnetizations, for the transverse anisotropic quantum XY model in one-, two-, and quasi two-dimension, for suitably chosen transverse fields and temperatures. The results have the potential for applications in decoherence effects in realizable quantum computers.

Low-Energy Properties of Aperiodic Quantum Spin Chains

Physical Review Letters, 2005

We investigate the low-energy properties of antiferromagnetic quantum XXZ spin chains with couplings following two-letter aperiodic sequences, by an adaptation of the Ma-Dasgupta-Hu renormalization-group method. For a given aperiodic sequence, we argue that in the easy-plane anisotropy regime, intermediate between the XX and Heisenberg limits, the general scaling form of the thermodynamic properties is essentially given by the exactly known XX behavior, providing a classification of the effects of aperiodicity on XXZ chains. As representative illustrations, we present analytical and numerical results for the low-temperature thermodynamics and the ground-state correlations for couplings following the Fibonacci quasiperiodic structure and a binary Rudin-Shapiro sequence, whose geometrical fluctuations are similar to those induced by randomness. PACS numbers: 75.10.Jm, 75.50.Kj At low temperatures, the interplay between lack of translational invariance and quantum fluctuations in lowdimensional strongly correlated electron systems may induce novel phases with peculiar behavior. In particular, randomness in quantum spin chains may lead, for instance, to Griffiths phases [1], large-spin formation , and random-singlet phases . On the other hand, studies on the influence of deterministic but aperiodic elements on similar systems (see e.g. ), inspired by the experimental discovery of quasicrystals, have revealed strong effects on dynamical and thermodynamic properties, but far less is known concerning the precise nature of the underlying ground-state phases.

Interaction-induced correlations and non-Markovianity of quantum dynamics

Physical Review A, 2013

We investigate the conditions under which the trace distance between two different states of a given open system increases in time due to the interaction with an environment, therefore signalling non-Markovianity. We find that the finite-time difference in trace distance is bounded by two sharply defined quantities that are strictly linked to the occurrence of system-environment correlations created throughout their interaction and affecting the subsequent evolution of the system. This allows to shed light on the origin of non-Markovian behaviours in quantum dynamics. We best illustrate our findings by tackling two physically relevant examples: a non-Markovian dephasing mechanism that has been the focus of a recent experimental endeavour and the open-system dynamics experienced by a spin connected to a finite-size quantum spin chain. PACS numbers: 03.65.Yz,03.65.Ta,42.50.Lc

Entanglement entropy in a periodically driven Ising chain

Journal of Statistical Mechanics: Theory and Experiment, 2016

In this work we study the entanglement entropy of a uniform quantum Ising chain in transverse field undergoing a periodic driving of period τ. By means of Floquet theory we show that, for any subchain, the entanglement entropy tends asymptotically to a value τperiodic in time. We provide a semi-analytical formula for the leading term of this asymptotic regime: It is constant in time and obeys a volume law. The entropy in the asymptotic regime is always smaller than the thermal one: because of integrability the system locally relaxes to a Generalized Gibbs Ensemble (GGE) density matrix. The leading term of the asymptotic entanglement entropy is completely determined by this GGE density matrix. Remarkably, the asymptotic entropy shows marked features in correspondence to some non-equilibrium quantum phase transitions undergone by a Floquet state analog of the ground state.

Many-body localized to ergodic transitions in a system with correlated disorder

Physical Review B

We study the transition from a many-body localized phase to an ergodic phase in spin chain with correlated random magnetic fields. Using multiple statistical measures like gap statistics and extremal entanglement spectrum distributions, we find the phase diagram in the disorder-correlation plane, where the transition happens at progressively larger values of the correlation with increasing values of disorder. We then show that one can use the average of sample variance of magnetic fields as a single parameter which encodes the effects of the correlated disorder. The distributions and averages of various statistics collapse into a single curve as a function of this parameter. This also allows us to analytically calculate the phase diagram in the disorder-correlation plane.

Equilibrium states of generic quantum systems subject to periodic driving

Physical review. E, Statistical, nonlinear, and soft matter physics, 2014

When a closed quantum system is driven periodically with period T, it approaches a periodic state synchronized with the drive in which any local observable measured stroboscopically approaches a steady value. For integrable systems, the resulting behavior is captured by a periodic version of a generalized Gibbs ensemble. By contrast, here we show that for generic nonintegrable interacting systems, local observables become independent of the initial state entirely. Essentially, this happens because Floquet eigenstates of the driven system at quasienergy ω(α) consist of a mixture of the exponentially many eigenstates of the undriven Hamiltonian, which are thus drawn from the entire extensive undriven spectrum. This is a form of equilibration which depends only on the Hilbert space of the undriven system and not on any details of its Hamiltonian.