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Many-body localization of spinless fermions with attractive interactions in one dimension

by Sheng-Hsuan Lin, B. Sbierski, F. Dorfner, C. Karrasch, F. Heidrich-Meisner

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Submission summary

Authors (as registered SciPost users): Christoph Karrasch · Björn Sbierski
Submission information
Preprint Link:  (pdf)
Date accepted: 2017-12-23
Date submitted: 2017-12-21 01:00
Submitted by: Karrasch, Christoph
Submitted to: SciPost Physics
Ontological classification
Academic field: Physics
  • Condensed Matter Physics - Theory
  • Quantum Physics
Approach: Theoretical


We study the finite-energy density phase diagram of spinless fermions with attractive interactions in one dimension in the presence of uncorrelated diagonal disorder. Unlike the case of repulsive interactions, a delocalized Luttinger-liquid phase persists at weak disorder in the ground state, which is a well-known result. We revisit the ground-state phase diagram and show that the recently introduced occupation-spectrum discontinuity computed from the eigenspectrum of one-particle density matrices is noticeably smaller in the Luttinger liquid compared to the localized regions. Moreover, we use the functional renormalization scheme to study the finite-size dependence of the conductance, which resolves the existence of the Luttinger liquid as well and is computationally cheap. Our main results concern the finite-energy density case. Using exact diagonalization and by computing various established measures of the many-body localization-delocalization transition, we argue that the zero-temperature Luttinger liquid smoothly evolves into a finite-energy density ergodic phase without any intermediate phase transition.

Author comments upon resubmission

We thank the Referee for their comments on our work. We are pleased
to see that the Referee states "... I'm in favor of publication in SciPost."

We thank the Refere for the two suggestions.

We added a discussion on the difference between our system of fermions with attractive
interactions versus the Bose-Hubbard model (where a mobilty edge seems to exist) to the
summary section. Phenomenologically, the superfluid phase in the case of bosons becomes
larger in parameter space in the presence of disorder, whereas in the case of fermions,
it shrinks when disorder is added. Moreover, in the case of the Bose-Hubbard model, heavy
particles such as doublons and even objects with more than 2 bosons per site exist, which
can give rise to slow dynamics already in the absence of disorder. These objects would
localize in the presence of disorder and they can be induced by increasing energy density.

As for the second comment, in our opinion there are no two separate MBL phases: what seems
to be two different MBL phases at weak disorder, separated by the ergodic phase at weak negative
V, becomes one connected MBL phase at strong disorder.

Published as SciPost Phys. 4, 002 (2018)

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