SciPost Phys. 7, 042 (2019) ·
published 3 October 2019
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Many-body localisation is studied in a disordered quantum spin-1/2 chain with
long-ranged power-law interactions, and distinct power-law exponents for
interactions between longitudinal and transverse spin components. Using a
self-consistent mean-field theory centring on the local propagator in Fock
space and its associated self-energy, a localisation phase diagram is obtained
as a function of the power-law exponents and the disorder strength of the
random fields acting on longitudinal spin-components. Analytical results are
corroborated using the well-studied and complementary numerical diagnostics of
level statistics, entanglement entropy, and participation entropy, obtained via
exact diagonalisation. We find that increasing the range of interactions
between transverse spin components hinders localisation and enhances the
critical disorder strength. In marked contrast, increasing the interaction
range between longitudinal spin components is found to enhance localisation and
lower the critical disorder.
Sthitadhi Roy, Ivan M. Khaymovich, Arnab Das, Roderich Moessner
SciPost Phys. 4, 025 (2018) ·
published 19 May 2018
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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
non-interacting particles subject to spatially quasiperiodic disorder.
Remarkably, this multifractality is robust in that it does not require any
fine-tuning 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 disorder-induced
enhancement of a superfluid transition.
