Localization due to interaction‐enhanced disorder in bosonic systems

Singh, Rajeev; Shimshoni, Efrat

doi:10.1002/andp.201600309

Cited by 7 publications

(9 citation statements)

References 53 publications

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“…In both cases, it has a peculiar feature that states which are above a certain energy threshold are localized whereas the states below are extended, so it may be called an 'inverted' mobility edge. This behavior has already been predicted for a two-and few-site bosonic systems in [55] with random on-site potentials.…”

Section: Localization Edgesupporting

confidence: 68%

Many-body localization of bosons in optical lattices

Sierant

Zakrzewski

2018

New J. Phys.

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Many-body localization for a system of bosons trapped in a one-dimensional lattice is discussed. Two models that may be realized for cold atoms in optical lattices are considered. The model with a random on-site potential is compared with previously introduced random interactions model. While the origin and character of the disorder in both systems is different they show interesting similar properties. In particular, many-body localization appears for a sufficiently large disorder as verified by a time evolution of initial density wave states as well as using statistical properties of energy levels for small system sizes. Starting with different initial states, we observe that the localization properties are energy-dependent which reveals an inverted many-body localization edge in both systems (that finding is also verified by statistical analysis of energy spectrum). Moreover, we consider computationally challenging regime of transition between many body localized and extended phases where we observe a characteristic algebraic decay of density correlations which may be attributed to subdiffusion (and Griffiths-like regions) in the studied systems. Ergodicity breaking in the disordered Bose-Hubbard models is compared with the slowing-down of the time evolution of the clean system at large interactions.

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Section: Localization Edgesupporting

confidence: 68%

Many-body localization of bosons in optical lattices

Sierant

Zakrzewski

2018

New J. Phys.

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“…This conclusion rules out the existence of an inverted mobility edge in our model, which may still exist in other disordered systems with superfluids present in the ground state, such as the Bose-Hubbard model. In fact, a series of very recent studies [42,43,84] indicates that there is an inverted mobility edge in the one-dimensional Bose-Hubbard model. This different behavior compared to our case of fermions with attractive interactions could be traced back to two observations.…”

Section: Resultsmentioning

confidence: 99%

“…In that experiment, evidence for a many-body localized regime at high energy densities was found, while (minding details of the specific disorder distribution realized in that experiment), theoretical studies predict a superfluid ground state [41], and thus an extended state, for the values of interaction strength and disorder for which the experiment reports localization. Theoretically, there is evidence for the existence of an inverted mobility edge in the one-dimensional Bose-Hubbard model [42,43]. Ref.…”

Section: Introductionmentioning

confidence: 99%

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

et al. 2018

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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 the one-particle density matrix is noticeably smaller in the Luttinger liquid compared to the localized regions. Moreover, we use the functional renormalization group scheme to study the finite-size dependence of the conductance, which also resolves the existence of the Luttinger liquid 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.

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“…All of this is discussed at length in the literature, see e.g. [27,11,20] Several authors have proposed that MBL should apply as well in systems without quenched disorder, in particular in translation-invariant systems, see [5,6,8,16,21,36,35,13,46,31,14,23,40], as the one studied in this paper. Whereas this issue is not settled yet, and in particular, we believe that this claim is false when taken literally [7,9] (see also the numerics in [30,43,4]), it is clear that a lot of localization phenomenology is present in such systems.…”

Section: Many-body Localization and Asymptotic Localizationmentioning

confidence: 95%

Asymptotic localization in the Bose-Hubbard model

Bols

Roeck

2018

Journal of Mathematical Physics

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We consider the Bose-Hubbard model. Our focus is on many-body localization, which was described by many authors in such models, even in the absence of disorder. Since our work is rigorous, and since we believe that the localization in this type of models is not strictly valid in the infinite-time limit, we necessarily restrict our study to 'asymptotic localization': We prove that transport and thermalization are small beyond perturbation theory in the limit of large particle density. Our theorem takes the form of a many-body Nekhoroshev estimate. An interesting and new aspect of this model is the following: even though our analysis proceeds by perturbation in the hopping, the localization can not be inferred from a lack of hybridization between zero-hopping eigenstates.

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Localization due to interaction‐enhanced disorder in bosonic systems

Cited by 7 publications

References 53 publications

Many-body localization of bosons in optical lattices

Many-body localization of bosons in optical lattices

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

Asymptotic localization in the Bose-Hubbard model

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