Emergence of anomalous dynamics from the underlying singular continuous spectrum in interacting many-body systems

Settino, Jessica; Talarico, N. W.; Cosco, Francesco; Plastina, Francesco; Maniscalco, Sabrina; Gullo, Nicola

doi:10.1103/physrevb.101.144303

Cited by 16 publications

(12 citation statements)

References 41 publications

(64 reference statements)

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“…The simplest quasiperiodic potential is the Aubry-André potential [23] [h i = h cos(2παi + φ)], in the presence of which the noninteracting system has extended or localized single-particle states depending on the potential strength h. For h < 2t all the single-particle energy eigenstates are extended, and for h > 2t all the energy eigenstates are localized, where t is the hopping parameter. Upon switching on interactions, this delocalized to localized transition transforms into a thermal-MBL transition where for h < h c all typical mid-spectrum states are thermal and for h > h c the typical states are many body localized [16,24].…”

mentioning

confidence: 99%

Transport in the nonergodic extended phase of interacting quasiperiodic systems

2020

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We study the transport properties and the spectral statistics of a one-dimensional closed quantum system of interacting spinless fermions in a quasiperiodic potential which produces a single-particle mobility edge in the absence of interaction. For such systems, it has been shown that the many-body eigenstates can be of three different kinds: extended and eigenstate thermalization hypothesis (ETH) obeying (thermal), localized and ETH violating (many body localized), and extended and ETH violating (nonergodic extended). Here we investigate the nonergodic extended phase from the point of view of level spacing statistics and charge transport. We calculate the dc conductivity and the low-frequency conductivity σ (ω) and show that both are consistent with subdiffusive transport. This is contrasted with diffusive transport in the thermal phase and blocked transport in the MBL phase.

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confidence: 99%

Transport in the nonergodic extended phase of interacting quasiperiodic systems

2020

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“…Though related with the AAH model, the non-interacting Fibonacci model is known to have very different transport properties, which continuously crosses over from ballistic to subdiffusive as a function of the strength of the potential [27,30]. There has been only few works exploring the Fibonacci model in presence of interactions [31,32,35]. In Ref.…”

Section: Discussionmentioning

confidence: 99%

“…Finally, a non equilibrium Green's functions approach in Ref. [35] suggests in the Fermi-Hubbard realization of the model a slow sub-diffusive behaviour at high potential strength, determined by the non-trivial spectral properties of the model.…”

Section: The Interacting Fibonacci Modelmentioning

confidence: 93%

“…A natural question, then, is what happens to the transport behavior of the Fibonacci model in presence of interactions? Different answers to this question have been proposed in the literature, ranging from a transition towards MBL [32], to metal-insulator transitions at low energies [33,34], to persistence of the anomalous diffusion [35]. Motivated by the lack of experimental results at this moment, in this paper, we focus on characterizing the transport of the interacting Fibonacci model with a further approach, exploiting dynamical quantum typicality [36,37].…”

Section: Introductionmentioning

confidence: 99%

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Quantum dynamics in the interacting Fibonacci chain

Chiaracane,

Pietracaprina,

Purkayastha

et al. 2021

Preprint

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Quantum dynamics on quasiperiodic geometries has recently gathered significant attention in ultra-cold atom experiments where non trivial localised phases have been observed. One such quasiperiodic model is the so called Fibonacci model. In this tight-binding model, non-interacting particles are subject to on-site energies generated by a Fibonacci sequence. This is known to induce critical states, with a continuously varying dynamical exponent, leading to anomalous transport. In this work, we investigate whether anomalous diffusion present in the non-interacting system survives in the presence of interactions and establish connections to a possible transition towards a localized phase. We investigate the dynamics of the interacting Fibonacci model by studying real-time spread of density-density correlations at infinite temperature using the dynamical typicality approach. We also corroborate our findings by calculating the participation entropy in configuration space and investigating the expectation value of local observables in the diagonal ensemble.

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“…A more detailed study of such a system and the relation between the time dependence of physical quantities and the nature of the support of the spectral function is reported in ref. .…”

Section: Quantum Quench In Fermionic Ultracold Gasesmentioning

confidence: 99%

A Scalable Numerical Approach to the Solution of the Dyson Equation for the Non‐Equilibrium Single‐Particle Green's Function

Talarico

Maniscalco

Gullo

2019

Physica Status Solidi (b)

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A numerical method to solve the set of Dyson-like equations in the framework of non-equilibrium Green's functions is presented. The technique is based on the self-consistent solution of the Dyson equations for the interacting single-particle Green's function once a choice for the self-energy, functional of the single-particle Green's function itself, is made. The authors briefly review the theory of the non-equilibrium Green's functions in order to highlight the main point useful in discussing the proposed technique. Then, the numerical implementation is presented and discussed, which is based on the distribution of the Keldysh components of the Green's function and the self-energy on a grid of processes. It is discussed how the structure of the considered self-energy approximations influences the distribution of the matrices in order to minimize the communication time among processes and which should be considered in the case of other approximations. The authors give an example of the application of this technique to the case of quenches in ultracold gases and to the single impurity Anderson model, also discussing the convergence and the stability features of the approach.

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Emergence of anomalous dynamics from the underlying singular continuous spectrum in interacting many-body systems

Cited by 16 publications

References 41 publications

Transport in the nonergodic extended phase of interacting quasiperiodic systems

Transport in the nonergodic extended phase of interacting quasiperiodic systems

Quantum dynamics in the interacting Fibonacci chain

A Scalable Numerical Approach to the Solution of the Dyson Equation for the Non‐Equilibrium Single‐Particle Green's Function

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