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.

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

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.

scholarly journals Finite-time quantum quenches in the XXZ Heisenberg chain

2019 ◽  
Vol 100 (11) ◽  
Author(s):  
Benedikt Schoenauer ◽  
Dirk Schuricht
Keyword(s):  
Finite Time ◽  
Heisenberg Chain ◽  
Time Quantum ◽  
Quantum Quenches

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 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 Quantum quenches in the transverse field Ising chain: II. Stationary state properties

2012 ◽  
Vol 2012 (07) ◽  
pp. P07022 ◽  
Author(s):  
Pasquale Calabrese ◽  
Fabian H L Essler ◽  
Maurizio Fagotti
Keyword(s):  
Stationary State ◽  
Transverse Field ◽  
Ising Chain ◽  
Quantum Quenches

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 Entanglement Dynamics of Random GUE Hamiltonians

2021 ◽  
Vol 10 (3) ◽  
Author(s):  
Daniel Chernowitz ◽  
Vladimir Gritsev
Keyword(s):  
Density Matrix ◽  
Spin Glass ◽  
Time Evolution ◽  
Random Matrices ◽  
Correlation Functions ◽  
Transverse Field ◽  
Reduced Density Matrix ◽  
Entanglement Dynamics ◽  
Point Correlation ◽  
Reduced Density

In this work, we consider a model of a subsystem interacting with a reservoir and study dynamics of entanglement assuming that the overall time-evolution is governed by non-integrable Hamiltonians. We also compare to an ensemble of Integrable Hamiltonians. To do this, we make use of unitary invariant ensembles of random matrices with either Wigner-Dyson or Poissonian distributions of energy. Using the theory of Weingarten functions, we derive universal average time evolution of the reduced density matrix and the purity and compare these results with several physical Hamiltonians: randomized versions of the transverse field Ising and XXZ models, Spin Glass and, Central Spin and SYK model. The theory excels at describing the latter two. Along the way, we find general expressions for exponential n-point correlation functions in the gas of GUE eigenvalues.

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