Dynamical conductivity and its fluctuations along the crossover to many-body localization

Barišić, O. S.; Kokalj, Jure; Balog, Ivan; Prelovšek, P.

doi:10.1103/physrevb.94.045126

Cited by 74 publications

(94 citation statements)

References 44 publications

(102 reference statements)

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“…Structure factor and relation to 1/ f noise.-The a.c. conductivity is closely related to the dynamic structure factor, Figure 2 recently, the (q, ω)-dependence of the structure factor was explored numerically across the MBL transition [68,69] as well as in bond-disordered spin systems with some analogies to MBL [70]. We note this spectral function can be a "noise" spectrum: if an external qubit couples to the operator O of the nearly MBL system-for instance, it has a Hamiltonian H q = σ z z /2 + σ x O-then the relaxation rate 1/T 1 of the qubit, given by a sum of Fermi's Golden rule rates of absorption and emission of the qubit due to fluctuations of the operator O, is given by the analogous structure factor S O (ω = z ).…”

Section: Griffiths Effects In One Dimension: Density and Current Respmentioning

confidence: 99%

Rare‐region effects and dynamics near the many‐body localization transition

et al. 2017

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The low-frequency response of systems near the many-body localization phase transition, on either side of the transition, is dominated by contributions from rare regions that are locally "in the other phase", i.e., rare localized regions in a system that is typically thermal, or rare thermal regions in a system that is typically localized. Rare localized regions affect the properties of the thermal phase, especially in one dimension, by acting as bottlenecks for transport and the growth of entanglement, whereas rare thermal regions in the localized phase act as local "baths" and dominate the low-frequency response of the MBL phase. We review recent progress in understanding these rare-region effects, and discuss some of the open questions associated with them: in particular, whether and in what circumstances a single rare thermal region can destabilize the many-body localized phase.

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Section: Griffiths Effects In One Dimension: Density and Current Respmentioning

confidence: 99%

Rare‐region effects and dynamics near the many‐body localization transition

et al. 2017

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“…is the most studied Many-Body-Localization model where numerical results for many observables are available [42][43][44][45][46][47][48][49][50][51][52][53] As explained in the Introduction, besides the usual periodic boundary conditions σ L+1 = σ 1 , it is interesting to consider twisted boundary conditions with some angle φ for the spin operators [21] …”

Section: Many-body-localization Models With Twisted Boundary Condmentioning

confidence: 99%

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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“…[20] (However, Ref. [34] shows that truly zero dc conductivity may require much larger disorder strength). First, we compare the quality of the plateaus as a function of the value of the corresponding Lagrange multiplier in the fMBL phase ( Fig.…”

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Accessing Many-Body Localized States through the Generalized Gibbs Ensemble

Inglis

Pollet

2016

Phys. Rev. Lett.

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We show how the thermodynamic properties of large many-body localized systems can be studied using quantum Monte Carlo simulations. To this end we devise a heuristic way of constructing local integrals of motion of very high quality, which are added to the Hamiltonian in conjunction with Lagrange multipliers. The ground state simulation of the shifted Hamiltonian corresponds to a high-energy state of the original Hamiltonian in case of exactly known local integrals of motion. We can show that the inevitable mixing between eigenstates as a consequence of non-perfect integrals of motion is weak enough such that the characteristics of many-body localized systems are not averaged out in our approach, unlike the standard ensembles of statistical mechanics. Our method paves the way to study higher dimensions and indicates that a full many-body localized phase in 2d, where (nearly) all eigenstates are localized, is likely to exist.Introduction -Many-body localization (MBL) addresses the fundamental question under which conditions quantum systems can avoid ergodicity and thermalization, thereby generalizing Anderson localization to interacting systems [1][2][3][4][5][6][7].The widely accepted mechanism for thermalization in quantum systems is the eigenstate thermalization hypothesis [8][9][10]: Under very mild assumptions, (almost) every eigenstate of the system is thermal. This implies that the reduced density matrix of a small subsystem, obtained by tracing out the degrees of freedom of the considered (eigen)state outside the subsystem, is indistinguishable from the thermal density matrix with an effective temperature that depends on the energy density of the chosen eigenstate. MBL states, on the contrary, retain knowledge of their initial local conditions in local operators for asymptotically large times. The picture of local integrals of motion (LIOM) [11][12][13][14][15][16] can explain most of the unusual phenomenology of MBL states: an area low holds in space leading to a logarithmic growth of the entanglement entropy in time and space, and the dc conductivity is identically zero. The area law was demonstrated explicitly in Ref. [17], while it was also found that rare regions can lead to deviations. Dynamics is a decisive characteristic to distinguish between thermal and MBL states: experiments on trapped ions [18] and 1d cold atoms [19] demonstrated memory of the initial conditions over long periods of time for sufficiently strong disorder.

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Dynamical conductivity and its fluctuations along the crossover to many-body localization

Cited by 74 publications

References 44 publications

Rare‐region effects and dynamics near the many‐body localization transition

Rare‐region effects and dynamics near the many‐body localization transition

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

Accessing Many-Body Localized States through the Generalized Gibbs Ensemble

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