Giuseppe De Tomasi, Mohsen Amini, Soumya Bera, Ivan M. Khaymovich, Vladimir E. Kravtsov
SciPost Phys. 6, 014 (2019) ·
published 30 January 2019

· pdf
We study analytically and numerically the dynamics of the generalized
RosenzweigPorter model, which is known to possess three distinct phases:
ergodic, multifractal and localized phases. Our focus is on the survival
probability $R(t)$, the probability of finding the initial state after time
$t$. In particular, if the system is initially prepared in a highlyexcited
nonstationary state (wave packet) confined in space and containing a fixed
fraction of all eigenstates, we show that $R(t)$ can be used as a dynamical
indicator to distinguish these three phases. Three main aspects are identified
in different phases. The ergodic phase is characterized by the standard
powerlaw decay of $R(t)$ with periodic oscillations in time, surviving in the
thermodynamic limit, with frequency equals to the energy bandwidth of the wave
packet. In multifractal extended phase the survival probability shows an
exponential decay but the decay rate vanishes in the thermodynamic limit in a
nontrivial manner determined by the fractal dimension of wave functions.
Localized phase is characterized by the saturation value of $R(t\to\infty)=k$,
finite in the thermodynamic limit $N\rightarrow\infty$, which approaches
$k=R(t\to 0)$ in this limit.
Sthitadhi Roy, Ivan M. Khaymovich, Arnab Das, Roderich Moessner
SciPost Phys. 4, 025 (2018) ·
published 19 May 2018

· pdf
Periodically driven, or Floquet, disordered quantum systems have generated
many unexpected discoveries of late, such as the anomalous Floquet Anderson
insulator and the discrete time crystal. Here, we report the emergence of an
entire band of multifractal wavefunctions in a periodically driven chain of
noninteracting particles subject to spatially quasiperiodic disorder.
Remarkably, this multifractality is robust in that it does not require any
finetuning of the model parameters, which sets it apart from the known
multifractality of $critical$ wavefunctions. The multifractality arises as the
periodic drive hybridises the localised and delocalised sectors of the undriven
spectrum. We account for this phenomenon in a simple random matrix based
theory. Finally, we discuss dynamical signatures of the multifractal states,
which should betray their presence in cold atom experiments. Such a simple yet
robust realisation of multifractality could advance this so far elusive
phenomenon towards applications, such as the proposed disorderinduced
enhancement of a superfluid transition.
Sthitadhi Roy, Ivan M. Khaymovich, Arnab Das, Roderich Moessner
SciPost Phys. 4, 025 (2018) ·
published 19 May 2018

· pdf
Periodically driven, or Floquet, disordered quantum systems have generated
many unexpected discoveries of late, such as the anomalous Floquet Anderson
insulator and the discrete time crystal. Here, we report the emergence of an
entire band of multifractal wavefunctions in a periodically driven chain of
noninteracting particles subject to spatially quasiperiodic disorder.
Remarkably, this multifractality is robust in that it does not require any
finetuning of the model parameters, which sets it apart from the known
multifractality of $critical$ wavefunctions. The multifractality arises as the
periodic drive hybridises the localised and delocalised sectors of the undriven
spectrum. We account for this phenomenon in a simple random matrix based
theory. Finally, we discuss dynamical signatures of the multifractal states,
which should betray their presence in cold atom experiments. Such a simple yet
robust realisation of multifractality could advance this so far elusive
phenomenon towards applications, such as the proposed disorderinduced
enhancement of a superfluid transition.
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