scholarly journals Spreading of entanglement and correlations after a quench with intertwined quasiparticles

2018 ◽  
Vol 5 (4) ◽  
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.

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

2017 ◽  
Vol 3 (3) ◽  
Author(s):  
Márton Kormos
Keyword(s):  
Scaling Limit ◽  
Transverse Field ◽  
Late Time ◽  
Ising Chain ◽  
Initial State ◽  
Equilibrium Dynamics ◽  
Time Scaling ◽  
Point Correlation ◽  
Lattice Effect ◽  
Non Equilibrium

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.

scholarly journals Full counting statistics in the transverse field Ising chain

2018 ◽  
Vol 4 (6) ◽  
Author(s):  
Stefan Groha ◽  
Fabian Essler ◽  
Pasquale Calabrese
Keyword(s):  
Characteristic Function ◽  
Transverse Field ◽  
Ising Chain ◽  
Gaussian States ◽  
Determinant Representation ◽  
Full Counting Statistics ◽  
Quantum Quenches ◽  
Temperature Equilibrium ◽  
Counting Statistics ◽  
Full Probability

We consider the full probability distribution for the transverse magnetization of a finite subsystem in the transverse field Ising chain. We derive a determinant representation of the corresponding characteristic function for general Gaussian states. We consider applications to the full counting statistics in the ground state, finite temperature equilibrium states, non-equilibrium steady states and time evolution after global quantum quenches. We derive an analytical expression for the time and subsystem size dependence of the characteristic function at sufficiently late times after a quantum quench. This expression features an interesting multiple light-cone structure.

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

2016 ◽  
Vol 1 (1) ◽  
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.

scholarly journals Entanglement and thermodynamics after a quantum quench in integrable systems

2017 ◽  
Vol 114 (30) ◽  
pp. 7947-7951 ◽  
Author(s):  
Vincenzo Alba ◽  
Pasquale Calabrese
Keyword(s):  
Scaling Limit ◽  
Entanglement Dynamics ◽  
Entanglement Evolution ◽  
Thermodynamic Entropy ◽  
Time Scaling ◽  
Quantum Quenches ◽  
Zero Entropy ◽  
Local Properties ◽  
Isolated Systems ◽  
Quasiparticle Picture

Entanglement and entropy are key concepts standing at the foundations of quantum and statistical mechanics. Recently, the study of quantum quenches revealed that these concepts are intricately intertwined. Although the unitary time evolution ensuing from a pure state maintains the system at zero entropy, local properties at long times are captured by a statistical ensemble with nonzero thermodynamic entropy, which is the entanglement accumulated during the dynamics. Therefore, understanding the entanglement evolution unveils how thermodynamics emerges in isolated systems. Alas, an exact computation of the entanglement dynamics was available so far only for noninteracting systems, whereas it was deemed unfeasible for interacting ones. Here, we show that the standard quasiparticle picture of the entanglement evolution, complemented with integrability-based knowledge of the steady state and its excitations, leads to a complete understanding of the entanglement dynamics in the space–time scaling limit. We thoroughly check our result for the paradigmatic Heisenberg chain.

scholarly journals Spread of Entanglement in Non-Relativistic Theories

2018 ◽  
Vol 2018 ◽  
pp. 1-27
Author(s):  
Sagar F. Lokhande
Keyword(s):  
Broad Class ◽  
Entanglement Entropy ◽  
Time Dependent ◽  
Quantum Field Theories ◽  
Strongly Coupled ◽  
Conformal Field ◽  
Instantaneous Power ◽  
Holographic Entanglement Entropy ◽  
Quantum Quenches ◽  
Good Order

We use a simple holographic toy model to study global quantum quenches in strongly coupled, hyperscaling-violating-Lifshitz quantum field theories using entanglement entropy as a probe. Generalizing our conformal field theory results, we show that the holographic entanglement entropy of small subsystems can be written as a simple linear response relation. We use this relation to derive a time-dependent first law of entanglement entropy. In general, this law has a time-dependent term resembling relative entropy which we propose as a good order parameter to characterize out-of-equilibrium states in the post-quench evolution. We use these tools to study a broad class of quantum quenches in detail: instantaneous, power law, and periodic.

scholarly journals Entanglement entropy in a periodically driven Ising chain

2016 ◽  
Vol 2016 (7) ◽  
pp. 073101 ◽  
Author(s):  
Angelo Russomanno ◽  
Giuseppe E Santoro ◽  
Rosario Fazio
Keyword(s):  
Entanglement Entropy ◽  
Ising Chain ◽  
Periodically Driven

Thermodynamics and spin correlations for an Ising chain in a random transverse field

1997 ◽  
Vol 76 (5) ◽  
pp. 855-858
Author(s):  
Oleg Derzhko ◽  
Taras Krokhmalskii ◽  
Taras Verkholyak
Keyword(s):  
Transverse Field ◽  
Ising Chain ◽  
Spin Correlations
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