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Spreading of entanglement and correlations after a quench with intertwined quasiparticles
by Alvise Bastianello, Pasquale Calabrese
This is not the current version.
|As Contributors:||Alvise Bastianello|
|Submitted by:||Bastianello, Alvise|
|Submitted to:||SciPost Physics|
|Subject area:||Quantum Physics|
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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Submission & Refereeing History
Reports on this Submission
Anonymous Report 2 on 2018-9-24 Invited Report
- Cite as: Anonymous, Report on arXiv:1807.10176v1, delivered 2018-09-24, doi: 10.21468/SciPost.Report.586
The paper is well written, topical, and has a clear message.
In the manuscript "Spreading of entanglement and correlations after a quench with intertwined quasiparticles" the authors consider the problem of describing in a semiclassical fashion the non-equilibrium post-quench dynamics of a system with multiple species of particles. The models they consider are quadratic, but where the pre-quench state of the system possess non-trivial pair correlations in momentum space. In describing the system semi-classically, the authors wish to show the a picture based on quasi-particle generation at the time of the quench and subsequent propagation is able to describe the growth of entanglement entropy and the evolution of the order parameter. As a test of their formalism, they consider quenches involving a quantum Ising model with a periodically varying transverse magnetic field in its ordered phase.
I think this paper is a useful contribution to our understanding of when and how a semiclassical picture can be used in the description of non-equilibrium dynamics of quantum systems. I particularly like the non-trivial extension of the quasi-particle picture to a case where correlations are present. I think this paper should be accepted for publication.
I do have one substantive comment that the authors may want to address:
In the treatment of quenches with an initial state that has non-trivial correlations, they still suppose that that effective set of quasi-particles does not see correlations between different momenta. Of course in fact in the example that they consider there are correlations between particles of different momenta because of the periodic nature of the transverse field and this inter-momenta correlations is subsequently "hidden" by partitioning the original Brillouin zone into n parts
(where n is the periodicity of the transverse field) and introducing a set of quasi-particles in this fragmented k-space.
My question is then do the authors think that finding a basis of effective quasi-particles where the correlations are only between different species of quasi-particles, but with same momentum, is a necessary condition for the quasi-particle picture to be valid. Could you, for example, initialize the Ising model in the ground state belonging to a random transverse field and then do the post-quench evolution in the periodic transverse field model considered in the paper and expect some formulation of the quasi-particle to work? Such an initial state would presumably involve correlations between different quasi-particle momenta. I am not looking for a definitive answer here (this would likely involve a whole new paper), but it would be interesting if the authors could comment on this possibility in the text of the current manuscript.
I spotted a number of minor typos:
Above Eqn. 2: "dragging" -> "deriving"
Below Eqn. 4: "originated" x 2 -> "originating" x 2
Below Eqn. 4: "considered" -> "considering"
Below Eqn. 4: "being their contribution" -> "their contribution being"
Below Eqn. 9: "can reside to" -> "can find"
Above Eqn. 53: "pose" -> "take as an ansatz"
page 13: "is drag at" -> "is dragged at"
Anonymous Report 1 on 2018-9-5 Invited Report
- Cite as: Anonymous, Report on arXiv:1807.10176v1, delivered 2018-09-05, doi: 10.21468/SciPost.Report.567
The paper describes the spreading of entanglement entropy following a quantum quench in the case in which the model Hamiltonian admits several quasi-particle excitations.
1) The paper is clearly written. 2) The semiclassical ansatz is well presented and supported by additional explicit calculations for a Ising-like chain. 3) The message is sharp and easy to understand. 4) The bibliography well prepared.
no specific points
In my opinion the paper contains interesting results. In some aspects this is a generalisation to the case of several types of excitations. It should be said that this generalisation contains some non-trivial aspects that are worth being published.