Integrals of motion for one-dimensional Anderson localized systems

Modak, Ranjan; Mukerjee, Subroto; Yuzbashyan, Emil A.; Shastry, B. Sriram

doi:10.1088/1367-2630/18/3/033010

Cited by 45 publications

(62 citation statements)

References 61 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: 80%

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: 80%

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

2016

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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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“…A priori, many-body localization and integrability are two independent concepts [41]. Despite this fact, integrable matrices do exhibit a parameter-dependent localization property [43] in which almost all eigenstates of the matrix H(x) = xT + V are localized in the basis of V for all values of x. The stability of this property when a random matrix perturbation is added to H(x), including the possibility of a multifractal phase accompanying the localized and delocalized regimes [40], is the subject of future study.…”

Section: Discussionmentioning

confidence: 99%

Integrable matrix theory: Level statistics

2016

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We study level statistics in ensembles of integrable $N\times N$ matrices linear in a real parameter $x$. The matrix $H(x)$ is considered integrable if it has a prescribed number $n>1$ of linearly independent commuting partners $H^i(x)$ (integrals of motion) $\left[H(x),H^i(x)\right] = 0$, $\left[H^i(x), H^j(x)\right]$ = 0, for all $x$. In a recent work, we developed a basis-independent construction of $H(x)$ for any $n$ from which we derived the probability density function, thereby determining how to choose a typical integrable matrix from the ensemble. Here, we find that typical integrable matrices have Poisson statistics in the $N\to\infty$ limit provided $n$ scales at least as $\log{N}$; otherwise, they exhibit level repulsion. Exceptions to the Poisson case occur at isolated coupling values $x=x_0$ or when correlations are introduced between typically independent matrix parameters. However, level statistics cross over to Poisson at $ \mathcal{O}(N^{-0.5})$ deviations from these exceptions, indicating that non-Poissonian statistics characterize only subsets of measure zero in the parameter space. Furthermore, we present strong numerical evidence that ensembles of integrable matrices are stationary and ergodic with respect to nearest neighbor level statistics.Comment: 18 pages, 26 figures, discussion on number variance added; published versio

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Integrals of motion for one-dimensional Anderson localized systems

Cited by 45 publications

References 61 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

Dynamical many-body localization in an integrable model

Integrable matrix theory: Level statistics

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