Quantum nonergodicity and fermion localization in a system with a single-particle mobility edge

Li, Xiaopeng; Pixley, J. H.; Deng, Dong-Ling; Ganeshan, Sriram; Sarma, S. Das

doi:10.1103/physrevb.93.184204

Cited by 104 publications

(110 citation statements)

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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: 81%

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: 81%

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

2016

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“…We call this phenomenon a 'many body localization proximity effect,' and it establishes that MBL is much more robust to coupling to an environment than was previously appreciated. It also suggests a possible explanation for the numerical results recently presented in [26,27], which counter-intuitively observed many body localization in an interacting model, when the non-interacting limit contained a single particle mobility edge.The system we consider consists of a D dimensional lattice which hosts two species of spinless fermions -c and d. The c fermions are present with density n c and have Hamiltonianwhere t c is the hopping, U is a nearest neighbor interaction, and ε is a random potential, drawn from a distribution of width W . The width of the distribution is sufficiently large that the c particles in isolation are in an MBL phase, with a localization length ξ c .…”

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confidence: 83%

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confidence: 83%

Many-body localization proximity effect

Nandkishore

2015

Phys. Rev. B

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We examine what happens when a strongly many body localized system is coupled to a weak heat bath, with both system and bath containing similar numbers of degrees of freedom. Previous investigations of localized systems coupled to baths operated in regimes where the back action of the system on the bath is negligible, and concluded that the bath generically thermalizes the system. In this work we show that when the system is strongly localized and the bath is only weakly ergodic, the system can instead localize the bath. We demonstrate this both in the limit of weak coupling between system and bath, and in the limit of strong coupling, and for two different types of 'weak' bath -baths which are close to an atomic limit, and baths which are close to a non-interacting limit. The existence of this 'many body localization proximity effect' indicates that many body localization is more robust than previously appreciated, and can not only survive coupling to a (weak) heat bath, but can even destroy the bath.Quantum localized systems violate many of the foundational assumptions of quantum statistical physics (such as the ergodic hypothesis), and present an exciting new frontier for research [1]. While localization was long believed to occur mainly in systems of non-interacting particles, the recent discovery of many body localization (MBL) [2][3][4][5] has ignited a blaze of interest in this field. It has been realized that quantum localized systems can display a cornucopia of exotic properties, including an emergent integrability [6][7][8], exotic quantum states of matter [9][10][11][12][13][14][15][16][17][18], and unexpected behavior in linear [19] and non-linear [20] response. These properties not only dramatically revise our understanding of quantum statistical physics, but also offer a new route to dissipationless quantum technologies. A summary of progress in this field can be found in the review article [21].Most works on MBL have focused on perfectly isolated quantum systems. Experimental systems, however, are always coupled (however weakly) to a thermalizing environment. The behavior of many body localized systems coupled to a thermalizing environment was first examined in [22][23][24], in the limit where back action on the bath was negligible and the bath could be treated as Markovian. In this limit, it was argued that an arbitrarily weak coupling to a thermodynamically large bath should restore ergodicity, thermalizing the system. These results suggested that perfect MBL would be unobservable in experiments, which would see instead only signatures of proximity to a localized phase. However, these works left open the question of whether different physics could result if the localization in the system were strong, and the bath were weak. Could many body localization then survive even after coupling to a heat bath?In this Letter, we show that when the system of interest is strongly localized, and the 'heat bath' is only weakly ergodic, then MBL in the system can not only survive coupling to the bath, but can e...

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“…Recent works have shown that the existence of integrals of motion (IOM) can be used as a diagnostic to quantify both noninteracting Anderson localization [26,27] and many-body localization [28][29][30]. In the context of dynamical localization for the model at hand, we work in the momentum basis and search for the existence of IOMs in this basis.…”

Section: Integrals Of Motionmentioning

confidence: 99%

Dynamical many-body localization in an integrable model

et al. 2016

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We investigate dynamical many-body localization and delocalization in an integrable system of periodicallykicked, interacting linear rotors. The linear-in-momentum Hamiltonian makes the Floquet evolution operator analytically tractable for arbitrary interactions. One of the hallmarks of this model is that depending on certain parameters, it manifests both localization and delocalization in momentum space. We present a set of "emergent" integrals of motion, which can serve as a fundamental diagnostic of dynamical localization in the interacting case. We also propose an experimental scheme, involving voltage-biased Josephson junctions, to realize such many-body kicked models.

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Quantum nonergodicity and fermion localization in a system with a single-particle mobility edge

Cited by 104 publications

References 97 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

Many-body localization proximity effect

Dynamical many-body localization in an integrable model

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