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Noise-induced transport in the Aubry-André-Harper model
by Devendra Singh Bhakuni, Talía L. M. Lezama and Yevgeny Bar Lev
This is not the latest submitted version.
|Authors (as registered SciPost users):||Yevgeny Bar Lev · Devendra Singh Bhakuni · Talía L. M. Lezama|
|Preprint Link:||scipost_202307_00026v1 (pdf)|
|Date submitted:||2023-07-20 16:07|
|Submitted by:||Bhakuni, Devendra Singh|
|Submitted to:||SciPost Physics|
We study quantum transport in a quasiperiodic Aubry-André-Harper (AAH) model induced by the coupling of the system to a Markovian heat bath. We find that coupling the heat bath locally does not affect transport in the delocalized and critical phases, while it induces logarithmic transport in the localized phase. Increasing the number of coupled sites at the central region introduces a transient diffusive regime, which crosses over to logarithmic transport in the localized phase and in the delocalized regime to ballistic transport. On the other hand, when the heat bath is coupled to equally spaced sites of the system, we observe a crossover from ballistic and logarithmic transport to diffusion in the delocalized and localized regimes, respectively. We propose a classical master equation, which captures our numerical observations for both coupling configurations on a qualitative level and for some parameters, even on a quantitative level. Using the classical picture, we show that the crossover to diffusion occurs at a time that increases exponentially with the spacing between the coupled sites, and the resulting diffusion constant decreases exponentially with the spacing.
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This paper seems to have solid and original results. They are not ground-breaking, but will be of interest to some other researchers working in this general area (such as myself).
I suggest a few changes to help with the clarity and completeness of the presentation:
The classical approximations that are developed in section IIIC appear to be only for the localized phase, which is fine. But this restriction should be explicitly stated where this is mentioned in the abstract, discussion and in section IIIC, since other parts of the paper also treat the critical and ballistic phases.
The study of the entanglement entropy uses an initial random product state. This initial state should be described more completely. Since another part of the paper uses an initial mixed state, here it should be said explicitly that an initial pure state is used. The ensemble from which this random pure product state is drawn should be explicitly stated. I suspect they mean initial local eigenstates of the occupation, randomly occupied or empty with equal probabilities for these two possibilities, but this must be explicit. Or are the initial local pure states uniformly sampled from the local Bloch sphere?
The caption of Fig. 2 should say what bath and couplings are being used (I did not find those details in the main text either).
Fig. 6(b), especially the lower trace, shows a possible odd/even effect vs lambda/2. Or is this all within the error bars? No error bars are shown in any of the figures. They should be roughly estimated and indicated, or where they are not visible this should be stated. This is crucial and required for any numerical work where the errors can be estimated (as they can here).
1)Numerical results are compared to phenomenological classical master equation, showing excellent agreement
2)Qualitative interpretation of the results clearly explained and discussed
1)Incremental with respect to previous literature, lack of major advance/breakthrough
2)Introduction and motivations can be improved
3)Results on entanglement entropy only for one type of system-bath coupling
This work studies transport in the Aubry-Andre'-Harper (AAH) model in presence of a Markovian dephasing bath. Different types of coupling geometries are considered. The focus is on spreading of density excitations (encoded in the root mean squared displacement) and partially on entanglement entropy.
The numerical results, obtained through a unitary unravelling of the Lindblad master equation, are well presented and interpreted through a classical master equation. The Authors find that when the coupling to the bath affects a finite portion of the chain transport at short times becomes diffusive, independent on disorder, while at longer time scales (outside of the zone of the influence of the bath) the usual transport behavior of the AAH is restored.
On the other hand, when the coupling to the bath is distributed among equally spaced sites diffusion emerges at long times.
I find this work interesting for those working in the field of disorder and dynamics. However I do not see the case for publication in Scipost Physics, based on its acceptance criteria. In particular I do not see a major result/breakthrough here. The work appears to be incremental with respect to previous literature (in particular Ref 58 from a subset of the authors, where similar analysis was done for the one dimensional Anderson model in presence of a local bath). I think the manuscript could be published in SciPostCore, provided the Authors address the points below.
1)Introduction and general motivations could be improved: why precisely the Authors are considering this type of coupling to the bath? What is the connection with MBL?Shouldn't thermal inclusions be somehow randomly distributed ?
2)Related question: in the conclusions the Authors mention their results provide an upper bound on transport in MBL. Why? How this comes about? Can the Authors elaborate on this point?
3)While the unravelling of the density matrix in Eq.5 is quite clear, it's less obvious how one should interpret Eq. 6, particularly given the Authors consider directly an infinite temperature density matrix. Is this correlation function averaged over the noise? Should this be equivalent to computing the same object through Linbdlad master equation because of some quantum regression theorem? It seems that some clarification is needed here.
4)Results on entanglement entropy are presented only in Fig 2, for the local (single-site) bath coupling? Why? As it is, this part seems quite decoupled from the rest of the article.
5)I am a bit surprised that a time-step dt=0.1 (in units of the hopping I guess?) is enough to have converged data and even more that averaging over N=10 trajectories is enough to converge to the Lindblad result. Could the Authors provide some supporting evidence?