# Universal Entanglement Dynamics following a Local Quench

### Submission summary

 As Contributors: Romain Vasseur Arxiv Link: http://arxiv.org/abs/1701.08866v3 (pdf) Date submitted: 2017-06-20 02:00 Submitted by: Vasseur, Romain Submitted to: SciPost Physics Academic field: Physics Specialties: Condensed Matter Physics - Theory Quantum Physics Approach: Theoretical

### Abstract

We study the time dependence of the entanglement between two quantum wires after suddenly connecting them via tunneling through an impurity. The result at large times is given by the well known formula $S(t) \approx {1\over 3}\ln {t}$. We show that the intermediate time regime can be described by a universal cross-over formula $S=F(tT_K)$, where $T_K$ is the crossover (Kondo) temperature: the function $F$ describes the dynamical "healing" of the system at large times. We discuss how to obtain analytic information about $F$ in the case of an integrable quantum impurity problem using the massless Form-Factors formalism for twist and boundary condition changing operators. Our results are confirmed by density matrix renormalization group calculations and exact free fermion numerics.

### Ontology / Topics

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Published as SciPost Phys. 3, 001 (2017)

### Author comments upon resubmission

Dear Editor,

We are glad that referees 1 and 3 think that we have addressed their comments in a satisfactory way, and we thank them for recommending publication. Referee 2 is concerned about the leading contribution’’ plotted in the main text being cherry-picked’’ among other terms. We argue below (and clarified in the main text) why we think this contribution is indeed dominant, even though the other terms are hard to evaluate numerically. Following the referee’s recommendations, we also added comments in the main text and appendix about the discarded terms. We believe we have been very honest about the pitfalls and shortcomings of our massless form factor approach. We do agree with the referee that further work would be needed to understand higher-order term contributions, and to clarify why the massless Form Factor program appears to be less controlled in this non-equilibrium setup. However, we still believe it is remarkable that this simple leading’’ contribution can capture this non-perturbative crossover accurately.

We feel we have taken into account and answered, to a more than reasonable extent,  the referees’ criticisms, and hope the paper can be accepted  soon.

Sincerely,
H. Saleur and R. Vasseur.

### List of changes

1) minor typos fixed throughout the paper
2) We added a discussion of the discarded terms’’ in the main text, both after eq 7 and in the discussion.
3) We clarified the appendix following Referee 2’s comments.