Drude weight fluctuations in many-body localized systems

Filippone, Michele; Brouwer, Piet W.; Eisert, Jens; Oppen, Felix von

doi:10.1103/physrevb.94.201112

Cited by 31 publications

(50 citation statements)

References 56 publications

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“…[23], the numerical results shown for the Many-Body-Localized phase are actually rather similar : on their Fig. 1, the heavy tail seems in reasonable agreement with the tail exponent of Eq.…”

Section: Many-body-localized Phase β =supporting

confidence: 72%

“…In Ref. [23], the authors have found numerically that the ergodic phase of the Many-BodyLocalization model is "in excellent agreement" non only with the tail of Eq. 25, but also with the RMT result of Eq.…”

Section: Statistical Properties Of the Dimensionless Curvature Kmentioning

confidence: 80%

“…So the dimensionless curvature k n of Eq. 13 based on the rescaling with the typical level spacing ∆ n involves a very different rescaling with the size L from the Drude weight D n studied in [23] …”

Section: Statistical Properties Of the Dimensionless Curvature Kmentioning

confidence: 99%

“…The case of the ground state energy in interacting quantum models has been analyzed both without disorder [18,19] and with disorder [20][21][22], in particular to characterize the persistent currents induced by a magnetic flux in mesoscopic rings. The case of highly excited eigenstates in a disordered model of interactions fermions has been investigated very recently [23] in the context of the Many-Body-Localization problem (see the recent reviews [24,25] and references therein). In the field of Many-BodyLocalization, the sensitivity of energy levels to a local perturbation of finite amplitude has been already proposed as a criterion for the MBL transition in [26] and discussed from the point of view of finite-size scaling in [27].…”

Section: Introductionmentioning

confidence: 99%

“…One goal of the present paper is thus to make the link between these works concerning a local perturbation of finite amplitude [26][27][28], and the infinitesimal perturbation introduced by the twist angle φ (Eq. 1) considered in [23].…”

Section: Introductionmentioning

confidence: 99%

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Many-body-localization transition: sensitivity to twisted boundary conditions

Monthus¹

2017

J. Phys. A: Math. Theor.

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For disordered interacting quantum systems, the sensitivity of the spectrum to twisted boundary conditions depending on an infinitesimal angle φ can be used to analyze the Many-Body-Localization Transition. The sensitivity of the energy levels En(φ) is measured by the level curvature Kn = E ′′ n (0), or more precisely by the Thouless dimensionless curvature kn = Kn/∆n, where ∆n is the level spacing that decays exponentially with the size L of the system. For instance ∆n ∝ 2 −L in the middle of the spectrum of quantum spin chains of L spins, while the Drude weight Dn = LKn studied recently by M. Filippone, P.W. Brouwer, J. Eisert and F. von Oppen [arXiv:1606.07291v1] involves a different rescaling. The sensitivity of the eigenstates |ψn(φ) > is characterized by the susceptibility χn = −F ′′ n (0) of the fidelity Fn = | < ψn(0)|ψn(φ) > |. Both observables are distributed with probability distributions displaying power-law tails2 , where β is the level repulsion index taking the values β GOE = 1 in the ergodic phase and β loc = 0 in the localized phase. The amplitudes A β and B β of these two heavy tails are given by some moments of the off-diagonal matrix element of the local current operator between two nearby energy levels, whose probability distribution has been proposed as a criterion for the Many-Body-Localization transition by M. Serbyn, Z. Papic and D.A. Abanin [Phys. Rev. X 5, 041047 (2015)].

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Section: Many-body-localized Phase β =supporting

confidence: 72%

Section: Statistical Properties Of the Dimensionless Curvature Kmentioning

confidence: 80%

Section: Statistical Properties Of the Dimensionless Curvature Kmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Many-body-localization transition: sensitivity to twisted boundary conditions

Monthus¹

2017

J. Phys. A: Math. Theor.

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Statistical properties of the Green function in finite size for Anderson localization models with multifractal eigenvectors

Monthus¹

2017

J. Phys. A: Math. Theor.

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For Anderson Localization models with multifractal eigenvectors on disordered samples containing N sites, we analyze in a unified framework the consequences for the statistical properties of the Green function. We focus in particular on the imaginary part of the Green function at coinciding points G I xx (E − iη) and study the scaling with the size N of the moments of arbitrary indices q when the broadening follows the scaling η = c N δ . For the standard scaling regime δ = 1, we find in the two limits c ≪ 1 and c ≫ 1 that the moments are governed by the anomalous exponents ∆(q) of individual eigenfunctions, without the assumption of strong correlations between the weights of consecutive eigenstates at the same point. For the non-standard scaling regimes 0 < δ < 1, we obtain that the imaginary Green function follows some Fréchet distribution in the typical region, while rare events are important to obtain the scaling of the moments. We describe the application to the case of Gaussian multifractality and to the case of linear multifractality.

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