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Particle fluctuations and the failure of simple effective models for many-body localized phases

by Maximilian Kiefer-Emmanouilidis, Razmik Unanyan, Michael Fleischhauer, Jesko Sirker

This is not the current version.

Submission summary

As Contributors: Michael Fleischhauer · Maximilian Kiefer-Emmanouilidis · Jesko Sirker
Preprint link: scipost_202111_00010v1
Date submitted: 2021-11-06 02:55
Submitted by: Kiefer-Emmanouilidis, Maximilian
Submitted to: SciPost Physics
Academic field: Physics
  • Atomic, Molecular and Optical Physics - Theory
  • Condensed Matter Physics - Theory
Approaches: Theoretical, Computational


We investigate and compare the particle number fluctuations in the putative many-body localized (MBL) phase of a spinless fermion model with potential disorder and nearest-neighbor interactions with those in the non-interacting case (Anderson localization) and in effective models where only interaction terms diagonal in the Anderson basis are kept. We demonstrate that these types of simple effective models cannot account for the particle number fluctuations observed in the MBL phase of the microscopic model. This implies that assisted and pair hopping terms---generated when transforming the microscopic Hamiltonian into the Anderson basis---cannot be neglected even at strong disorder and weak interactions. As a consequence, it appears questionable if the microscopic model possesses an exponential number of exactly conserved {\it local} charges. If such a set of conserved local charges does not exist, then particles are expected to ultimately delocalize for any finite disorder strength.

Current status:
Has been resubmitted

Author comments upon resubmission

We would like to thank both referees for the very
careful and thorough evaluation of our work and the helpful
comments. In the following, we provide a detailed and point-by-point reply.
Accordingly, we have modified our manuscript and followed
most of the suggestions made.

List of changes

1) Below Eq. (1) we added: “Note that in contrast to Bethe ansatz integrable systems which have only linearly many independent local charges, any combination of operators ηi which are centered near a lattice site n is again a new local conserved charge [8]. For a fully localized system there are as many independent local charges as there are eigenstates.“

2) Page 2, second paragraph. We elude further on the generality of the obtained results and the results by Imbrie by adding: “We note, furthermore, that while a fully controlled Schrieffer-Wolff type transformation from a microscopic quantum spin chain with disorder to an effective model as in Eq. (1) has been claimed to be proven in Refs. [11, 12], these results are currently under debate. Here we will concentrate on one particular numerical scheme which has been used, for example, in Ref. [34] but we will argue that the qualitative findings are generic: even if the orbitals ηn are further renormalized, the number fluctuations have to remain strictly bounded as long as the η-orbitals remain local.“

3) Page 3, second sentence. We added a sentence and a reference about a different interpretation of unbound particle fluctuations “An unbounded growth of particle fluctuations was also noticed by Weiner et al. [33], here the authors suggested an additional phase which is located between the thermal and the MBL phase.”

4) Page 3, section 3.3 and Fig.5, we improved on some minor notation issues concerning the particle number fluctuations \Delta N^2 (t).

5) Page 4, details about the numerical method added: “We carry out all of these steps for each disorder realization separately by using exact diagonalization (ED). The number of disorder configurations is then increased till the considered averages are converged on the scales the results are presented on.“

6) Below Eq. (10): “Here we want to also stress that this qualitative picture is general and independent of the specific effective model considered. It does hold with some finite length scale \xi_0 as long as the \eta-orbitals are local.”

7) The conclusions have been reformulated. We comment now, in particular, on the criticism of our previous results by Luitz and Bar Lev and on the very recent results which have revised the critical disorder strength in the considered microscopic model from Dc ~ 16 to Dc > 80.

8) We have added references to three papers, Refs. [12], [33], [51], and [52].

9) We added a note about the color coding of Figs 1,3,5

10) We have added insets to Figs. 2(b), 4(b), 6(b), 2(d),4(d), and 6(d) and mention this in the captions of the corresponding figures.

11) We mention in figure 11 that common free fermion methods have been used.

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