|Title:||Inhomogeneous quenches in the transverse field Ising chain: scaling and front dynamics|
|As Contributors:||Márton Kormos|
|Submitted by:||Kormos, Márton|
|Submitted to:||SciPost Physics|
|Subject area:||Quantum Physics|
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.
I submit the revised version of the manuscript, following the suggestions of the referees who found my work "interesting" and of high significance. All the referees made valid and very useful comments and asked relevant questions. I believe I managed to answer all the questions and I have implemented the requested changes. In particular, I extended the discussions of the results at several places. Thanks to the remarks of the referees the paper has definitely improved.
As all three referees recommended the publication of the manuscript after minor revision, I hope that the new version meets all the criteria for publication in SciPost.
List of changes (typos or minor changes are not included):
Changed the abstract, introduction, and conclusion. References to main results (equations and figures) included in the Conclusions to improve readability.
Added refs. [42,47,48,68,69,70,72,75].
Connection made with Ref.  in he Introduction and Sec. 4 (in the first paragraph, below Eq. (37) and below Eq. (39)).
Remark added at the end of Sec. 5.1. about the leading corrections at finite $x/t$.
Remark added at the end of Sec. 5.1. and in the Conclusions about the possible implications of the lattice effect showing up in the leading corrections to the NESS.
Paragraph added below Eq. (55) about the universal nature of the Airy kernel.
Paragraph added below Eq. (56) discussing the correlations that are not described by the Airy kernel near the front (e.g. the fermion density in the ferromagnetic phase).
Changed the derivation of the front structure in Sec 5.2 to correctly take into account the finite asymptotic value of correlations outside the light cone.
Added subsection 5.2.2. on the edge behavior in the critical case.
Added footnote 7 making it clear that the boundary edge mode was included in the numerical calculation for $h<1$.
Changed Fig. 1a and 2b to show the critical case.
The author has carefully considered all the remarks raised by the referees and revised the manuscript accordingly.