Inhomogeneous quenches in the transverse field Ising chain: scaling and front dynamics

We investigate the non-equilibrium dynamics of the transverse field quantum Ising chain evolving from an inhomogeneous initial state given by joining two macroscopically different semi-infinite chains. We obtain integral expressions for all two-point correlation functions of the Jordan--Wigner Majorana fermions at any time and for any value of the transverse field. Using this result, we analytically compute the profiles of various physical observables in the space-time scaling limit and show that they can be obtained from a hydrodynamic picture based on ballistically propagating quasiparticles. Going beyond the hydrodynamic limit, we analyze the approach to the non-equilibrium steady state and find that the leading late time corrections display a lattice effect. We also study the fine structure of the propagating fronts which are found to be described by the Airy kernel and its derivatives. Near the front we observe the phenomenon of energy back-flow where the energy locally flows from the colder to the hotter region.

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Spreading of entanglement and correlations after a quench with intertwined quasiparticles

10.21468/scipostphys.5.4.033 ◽

2018 ◽

Vol 5 (4) ◽

Cited By ~ 15

Author(s):

Alvise Bastianello ◽

Pasquale Calabrese

Keyword(s):

Entanglement Entropy ◽

Scaling Limit ◽

Lattice Models ◽

Transverse Field ◽

Ising Chain ◽

Perfect Agreement ◽

Pair Correlations ◽

Hamiltonian Parameter ◽

Time Scaling ◽

Quantum Quenches

We extend the semiclassical picture for the spreading of entanglement and correlations to quantum quenches with several species of quasiparticles that have non-trivial pair correlations in momentum space. These pair correlations are, for example, relevant in inhomogeneous lattice models with a periodically-modulated Hamiltonian parameter. We provide explicit predictions for the spreading of the entanglement entropy in the space-time scaling limit. We also predict the time evolution of one- and two-point functions of the order parameter for quenches within the ordered phase. We test all our predictions against exact numerical results for quenches in the Ising chain with a modulated transverse field and we find perfect agreement.

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Time evolution during and after finite-time quantum quenches in the transverse-field Ising chain

10.21468/scipostphys.1.1.003 ◽

2016 ◽

Vol 1 (1) ◽

Cited By ~ 30

Author(s):

Tatjana Puskarov ◽

Dirk Schuricht

Keyword(s):

Time Evolution ◽

Finite Time ◽

Transverse Field ◽

Transverse Magnetic ◽

Ising Chain ◽

Continuous Change ◽

Time Quantum ◽

Quantum Quenches ◽

Point Correlation ◽

Loschmidt Echo

We study the time evolution in the transverse-field Ising chain subject to quantum quenches of finite duration, ie, a continuous change in the transverse magnetic field over a finite time. Specifically, we consider the dynamics of the total energy, one- and two-point correlation functions and Loschmidt echo during and after the quench as well as their stationary behaviour at late times. We investigate how different quench protocols affect the dynamics and identify universal properties of the relaxation.

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Non-equilibrium dynamics in the random bond Ising chain: A reminiscence of aging in spin glasses

Physica A Statistical Mechanics and its Applications ◽

10.1016/0378-4371(94)90081-7 ◽

1994 ◽

Vol 210 (3-4) ◽

pp. 326-340 ◽

Cited By ~ 7

Author(s):

H. Rieger ◽

J. Kisker ◽

M. Schreckenberg

Keyword(s):

Spin Glasses ◽

Ising Chain ◽

Equilibrium Dynamics ◽

Non Equilibrium

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Study of the time evolution of correlation functions of the transverse Ising chain with ring frustration by perturbative theory

Modern Physics Letters B ◽

10.1142/s021798491850121x ◽

2018 ◽

Vol 32 (10) ◽

pp. 1850121

Author(s):

Zhen-Yu Zheng ◽

Peng Li

Keyword(s):

Correlation Function ◽

Schrödinger Equation ◽

Time Evolution ◽

Correlation Functions ◽

Schrodinger Equation ◽

Transverse Field ◽

Time Dependent ◽

Ising Chain ◽

Point Correlation ◽

Point Correlation Function

We consider the time evolution of two-point correlation function in the transverse-field Ising chain (TFIC) with ring frustration. The time-evolution procedure we investigated is equivalent to a quench process in which the system is initially prepared in a classical kink state and evolves according to the time-dependent Schrödinger equation. Within a framework of perturbative theory (PT) in the strong kink phase, the evolution of the correlation function is disclosed to demonstrate a qualitatively new behavior in contrast to the traditional case without ring frustration.

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On computing non-equilibrium dynamics following a quench

SciPost Physics ◽

10.21468/scipostphys.11.6.104 ◽

2021 ◽

Vol 11 (6) ◽

Author(s):

Neil Robinson ◽

Albertus de Klerk ◽

Jean-Sébastien Caux

Keyword(s):

Numerical Approach ◽

Solvable Models ◽

Lattice Systems ◽

Initial State ◽

Numerical Renormalization Group ◽

Equilibrium Dynamics ◽

Quantum Quench ◽

Truncation Scheme ◽

Exactly Solvable ◽

Non Equilibrium

Computing the non-equilibrium dynamics that follows a quantum quench is difficult, even in exactly solvable models. Results are often predicated on the ability to compute overlaps between the initial state and eigenstates of the Hamiltonian that governs time evolution. Except for a handful of known cases, it is generically not possible to find these overlaps analytically. Here we develop a numerical approach to preferentially generate the states with high overlaps for a quantum quench starting from the ground state or an excited state of an initial Hamiltonian. We use these preferentially generated states, in combination with a "high overlap states truncation scheme" and a modification of the numerical renormalization group, to compute non-equilibrium dynamics following a quench in the Lieb-Liniger model. The method is non-perturbative, works for reasonable numbers of particles, and applies to both continuum and lattice systems. It can also be easily extended to more complicated scenarios, including those with integrability breaking.

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Temperature chaos is present in off-equilibrium spin-glass dynamics

Communications Physics ◽

10.1038/s42005-021-00565-9 ◽

2021 ◽

Vol 4 (1) ◽

Author(s):

Marco Baity-Jesi ◽

Enrico Calore ◽

Andrés Cruz ◽

Luis Antonio Fernandez ◽

José Miguel Gil-Narvion ◽

...

Keyword(s):

Spin Glass ◽

Dynamic Effect ◽

Large Degree ◽

Equilibrium Temperature ◽

Experimental Conditions ◽

Temperature Changes ◽

Equilibrium Dynamics ◽

Glass Dynamics ◽

Extreme Sensitivity ◽

Non Equilibrium

AbstractExperiments featuring non-equilibrium glassy dynamics under temperature changes still await interpretation. There is a widespread feeling that temperature chaos (an extreme sensitivity of the glass to temperature changes) should play a major role but, up to now, this phenomenon has been investigated solely under equilibrium conditions. In fact, the very existence of a chaotic effect in the non-equilibrium dynamics is yet to be established. In this article, we tackle this problem through a large simulation of the 3D Edwards-Anderson model, carried out on the Janus II supercomputer. We find a dynamic effect that closely parallels equilibrium temperature chaos. This dynamic temperature-chaos effect is spatially heterogeneous to a large degree and turns out to be controlled by the spin-glass coherence length ξ. Indeed, an emerging length-scale ξ* rules the crossover from weak (at ξ ≪ ξ*) to strong chaos (ξ ≫ ξ*). Extrapolations of ξ* to relevant experimental conditions are provided.

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Epidemic growth and Griffiths effects on an emergent network of excited atoms

Nature Communications ◽

10.1038/s41467-020-20333-7 ◽

2021 ◽

Vol 12 (1) ◽

Author(s):

T. M. Wintermantel ◽

M. Buchhold ◽

S. Shevate ◽

M. Morgado ◽

Y. Wang ◽

...

Keyword(s):

Complex Systems ◽

Power Laws ◽

Excitation Density ◽

Griffiths Phase ◽

Many Body ◽

Excited Atoms ◽

Equilibrium Dynamics ◽

Many Body Systems ◽

Excitation Number ◽

Non Equilibrium

AbstractWhether it be physical, biological or social processes, complex systems exhibit dynamics that are exceedingly difficult to understand or predict from underlying principles. Here we report a striking correspondence between the excitation dynamics of a laser driven gas of Rydberg atoms and the spreading of diseases, which in turn opens up a controllable platform for studying non-equilibrium dynamics on complex networks. The competition between facilitated excitation and spontaneous decay results in sub-exponential growth of the excitation number, which is empirically observed in real epidemics. Based on this we develop a quantitative microscopic susceptible-infected-susceptible model which links the growth and final excitation density to the dynamics of an emergent heterogeneous network and rare active region effects associated to an extended Griffiths phase. This provides physical insights into the nature of non-equilibrium criticality in driven many-body systems and the mechanisms leading to non-universal power-laws in the dynamics of complex systems.

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