Many-Body Localization in the Presence of a Single-Particle Mobility Edge

Modak, Ranjan; Mukerjee, Subroto

doi:10.1103/physrevlett.115.230401

Cited by 130 publications

(130 citation statements)

References 46 publications

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“…However, due to large finite size effects these studies are inconclusive with respect to localization [13][14][15][16][17][18][19][20]. A related question, whether MBL can exist in a system where only some of the single-particle states are delocalized, namely in systems with a mobility edge in the singleparticle spectrum, has been affirmatively answered [21][22][23][24]. In our work, we go one step beyond, and completely abolish the assumption of localization of single-particle states.…”

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confidence: 79%

Many-body localization in system with a completely delocalized single-particle spectrum

2016

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Many-body localization (MBL) in a one-dimensional Fermi Hubbard model with random on-site interactions is studied. While for this model all single-particle states are trivially delocalized, it is shown that for sufficiently strong disordered interactions the model is many-body localized. It is therefore argued that MBL does not necessary rely on localization of the single-particle spectrum. This model provides a convenient platform to study pure MBL phenomenology, since Anderson localization in this model does not exist. By examining various forms of the interaction term a dramatic effect of symmetries on charge transport is demonstrated. A possible realization in a cold atom experiments is proposed. Introduction.-It has been known for almost 60 years that non-interacting particles in one-dimensional disordered systems exhibit Anderson localization [1]. Transport in these systems is exponentially suppressed with the system size, and without coupling to the environment, these systems are non-ergodic at any temperature. Anderson localized systems are, however, non-generic, since they do not include interactions which allow for the exchange of energy. For many years it was assumed that interactions generally restore ergodicity and destroy localization [2]. A decade ago, using non-equilibrium diagrammatic techniques, it was argued that Anderson localization is stable under the addition of a small shortranged interactions [3], a phenomenon currently known as many-body localization (MBL). Many-body localized systems are the only known generic non-ergodic systems which do not follow the assumptions of statistical mechanics [4][5][6]. While the realization of MBL systems presents challenges in condensed matter systems due to inevitable presence of phonons [7,8], recent experiments in cold atoms have provided evidence of the existence of MBL in both one-dimensional [9-11] and two-dimensional systems [12].

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confidence: 79%

Many-body localization in system with a completely delocalized single-particle spectrum

2016

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“…4,22 Our work has implications for the localization properties of other systems which have single particle mobility edges. Other groups 5,6 have claimed, in the context of a quasiperiodic one dimensional model with localized and extended single particle states (both of which scale with system size), that with the introduction of interactions, MBL can still occur. Our work is for a two-dimensional system with quenched disorder with a sub-thermodynamic (but divergent in the thermodynamic limit) number of single-particle eigenstates.…”

Section: Discussionmentioning

confidence: 99%

“…Early numerical work 4 showed the existence of such a phenomenon at intermediate disorder strengths, essentially due to the fact that the localization transition happens at different disorder strengths as a function of energy density. Other works 5,6 have presented numerical evidence that if one starts with a system with a single-particle mobility edge (i.e. the single particle spectrum has a finite fraction of extended states), adding interactions can give a many-body mobility edge.…”

Section: Introductionmentioning

confidence: 99%

Absence of many-body localization in a single Landau level

Geraedts

Bhatt

2017

Phys. Rev. B

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The localization properties of the highly excited states of a system projected into a single Landau level are analyzed. An analysis of level spacing ratios for finite size systems shows a clear crossover from extend (GUE) to localized (Poisson) statistics, indicating a many body localization transition. However, the location of this transition depends very strongly on system size, and appears to scale to infinite disorder in the thermodynamic limit. This result does not depend on the properties of the ground state (such as whether the ground state exhibits topological order), as expected for a transition of highly-excited eigenstates. We therefore conclude that many body localization does not exist in these systems. Our results demonstrate that a sub-thermodynamic number of single particle effectively extended states is sufficient to cause all many body states to become extended.

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“…The eigenstates of a many-body localized system are connected to the eigenstates of the Anderson insulator by a finite-depth local unitary transformation [13]. Recent work [25][26][27] has raised the question of whether MBL can also exist in a system where in the non-interacting limit, a critical single-particle energy, the mobility edge, separates localized and delocalized states. In one dimension, this can be achieved in certain types of quasi-disordered systems, and it is a generic scenario in higher dimensions.…”

Section: Introductionmentioning

confidence: 99%

Many-body localization in the presence of a small bath

et al. 2017

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In the presence of strong disorder and weak interactions, closed quantum systems can enter a many-body localized phase where the system does not conduct, does not equilibrate even for arbitrarily long times, and robustly violates quantum statistical mechanics. The starting point for such a many-body localized phase is usually taken to be an Anderson insulator where, in the limit of vanishing interactions, all degrees of freedom of the system are localized. Here, we instead consider a model where in the non-interacting limit, some degrees of freedom are localized while others remain delocalized. Such a system can be viewed as a model for a many-body localized system brought into contact with a small bath of a comparable number of degrees of freedom. We numerically and analytically study the effect of interactions on this system and find that generically, the entire system delocalizes. However, we find certain parameter regimes where results are consistent with localization of the entire system, an effect recently termed many-body proximity effect.

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Many-Body Localization in the Presence of a Single-Particle Mobility Edge

Cited by 130 publications

References 46 publications

Many-body localization in system with a completely delocalized single-particle spectrum

Many-body localization in system with a completely delocalized single-particle spectrum

Absence of many-body localization in a single Landau level

Many-body localization in the presence of a small bath

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