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

by Márton Kormos

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Submission summary

As Contributors: Márton Kormos
Arxiv Link: (pdf)
Date accepted: 2017-08-28
Date submitted: 2017-08-23 02:00
Submitted by: Kormos, Márton
Submitted to: SciPost Physics
Academic field: Physics
  • Condensed Matter Physics - Theory
  • Quantum Physics
Approach: Theoretical


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 compute analytically 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.

Ontology / Topics

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Airy kernel Generalized hydrodynamics (GHD) Jordan-Wigner fermions/transformation Majorana fermions Out-of-equilibrium systems Quantum quenches Spatially inhomogeneous systems Transverse-field Ising chain

Published as SciPost Phys. 3, 020 (2017)

Author comments upon resubmission

Dear Editor,

I resubmit my manuscript in which I have implemented all the minor changes requested by Referee 2.

Kind regards,
Marton Kormos

List of changes

1. Ref. [75] is now cited in Sec. 5.2.2, at the end of Sec. 6.2 and in Sec. 8 related to the edge behavior in the critical case.

2. The condition for the appearance of bound states after Eq. (11) is corrected and a footnote is added.

3. In Sec. 5.2 "density of Majorana fermions" is replaced by "density of Jordan-Wigner fermions".

4. A sentence regarding the critical edge scaling in the last paragraph of Sec. 5.2.2 is changed.

5. The requirement of vanishing anomalous correlations in the initial state is mentioned at the beginning of the Conclusions.

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