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Transient Features in Charge Fractionalization, Local Equilibration and Non-equilibrium Bosonization

by Alexander Schneider, Mirco Milletari, Bernd Rosenow

Submission summary

As Contributors: Mirco Milletari
Arxiv Link: (pdf)
Date accepted: 2017-02-08
Date submitted: 2016-12-14 01:00
Submitted by: Milletari, Mirco
Submitted to: SciPost Physics
Academic field: Physics
  • Condensed Matter Physics - Theory
  • Mathematical Physics
  • Quantum Physics
Approach: Theoretical


In quantum Hall edge states and in other one-dimensional interacting systems, charge fractionalization can occur due to the fact that an injected charge pulse decomposes into eigenmodes propagating at different velocities. If the original charge pulse has some spatial width due to injection with a given source-drain voltage, a finite time is needed until the separation between the fractionalized pulses is larger than their width. In the formalism of non-equilibrium bosonization, the above physics is reflected in the separation of initially overlapping square pulses in the effective scattering phase. When expressing the single particle Green's function as a functional determinant of counting operators containing the scattering phase, the time evolution of charge fractionalization is mathematically described by functional determinants with overlapping pulses. We develop a framework for the evaluation of such determinants, describe the system's equilibration dynamics, and compare our theoretical results with recent experimental findings.

Ontology / Topics

See full Ontology or Topics database.

Bosonization Charge fractionalization Fractionalization Non-equilibrium bosonization One-dimensional systems Quantum Hall edge states Quantum Hall effect

Published as SciPost Phys. 2, 007 (2017)

Submission & Refereeing History

Reports on this Submission

Anonymous Report 1 on 2017-1-14 (Invited Report)

  • Cite as: Anonymous, Report on arXiv:1610.02036v3, delivered 2017-01-14, doi: 10.21468/SciPost.Report.63






The analysis presented in this work is, to a large extent, of technical nature. I would like to commend the authors for being able to get their message(s) through, even for those readers who may not follow in detail each and every step of the derivation.

The authors’ two main thrusts are: (i) extend previous analyses of non-equilibrium bosonization. Specifically, the time evolution of injected charge is formally described by functional determinants with overlapping square pulses which describe the effective scattering phase. Unlike in the “semiclassical limit”, where those pulses are non-overlapping, here a full-fledged quantum mechanical treatment is required, and is developed by the authors. (ii) apply non-equilibrium bosonization (in this fully quantum limit) to the problem of electron fractionalization. Specifically, the authors address the transient behavior of fractionalization at the edge of \nu=2 integer QHE system, and compare their analysis to experimental data.

These are clearly significant contributions in this important field of non-equilibrium quantum electronic matter. As a further added value of this work, I would mention its clarity and the fact that the analysis is well embedded in a broad context of earlier works (on bosonization and on fractionaliation). I could easily see how the introduction of this paper is extended into a review of the field…

I therefore strongly recommend this work for publication.

Requested changes

Two items the authors ** may** want to consider (but should not constitute a condition for publication): First, in the introduction the authors refer to “recently developed non-equilibrium bosonization” and provide a list of references. In fac, non-equilibrium bosonization was first developed in Ref. 16 (and to some extent also in D.B. Gutman, et al, Phys. Rev.Lett. 2008) before the other references mentioned in the Introduction. Second, it would be intriguing to think how the results presented here should apply to more complex edges, e.g., the edge of a fractional bulk filling fraction (e.g., the $\nu=2/3$ FQHE), which has been recently studied experimentally.

  • validity: top
  • significance: high
  • originality: high
  • clarity: top
  • formatting: perfect
  • grammar: perfect

Author:  Mirco Milletari  on 2017-02-24  [id 104]

(in reply to Report 1 on 2017-01-14)
answer to question
suggestion for further work

We would like to thank the referee for his/her valuable comments and for recommending our paper for publication in SciPost. We are pleased to learn that the referee found our contribution “clearly significant”. Below we address the referee’s comments.

As for the First comment, we thank the referee for pointing to us the missing reference. We have modified the manuscript accordingly.

Concerning the Second comment, it would be indeed intriguing to think how our results generalise to more complex edges, e.g., the edge of a fractional bulk filling fraction (e.g., the ν=2/3 FQHE). Although the interferometer setup with edges at fractional filling fractions bear similarities with the problem considered in our paper, there are few important differences:

In our problem, we used the fact that the system before the first quantum point contact was non-interacting. Although this point seems crucial for the Quantum Quench model to work, it is possible to get around this restriction by using the original functional Keldysh approach developed in Ref. 16. We believe that this would allow to generalise our results to the case of Fractional filling fractions.
For the composite fractional edge, one would expect the existence of additional constraints on the dynamics of the system coming from its non-trivial topology. It would be certainly intriguing to understand the interplay of topology and strong non-equilibrium in this setup.

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