Xhek Turkeshi, Damien Barbier, Leticia F. Cugliandolo, Marco Schirò, Marco Tarzia
SciPost Phys. 12, 189 (2022) ·
published 9 June 2022
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We discuss and compare two recently proposed toy models for anomalous
transport and Griffiths effects in random systems near the Many-Body
Localization transitions: the random dephasing model, which adds thermal
inclusions in an Anderson Insulator as local Markovian dephasing channels that
heat up the system, and the random Gaussian Orthogonal Ensemble (GOE) approach
which models them in terms of ensembles of random regular graphs. For these two
settings we discuss and compare transport and dissipative properties and their
statistics. We show that both types of dissipation lead to similar
Griffiths-like phenomenology, with the GOE bath being less effective in
thermalising the system due to its finite bandwidth. We then extend these
models to the case of a quasi-periodic potential as described by the
André-Aubry-Harper model coupled to random thermal inclusions, that we show
to display, for large strength of the quasiperiodic potential, a similar
phenomenology to the one of the purely random case. In particular, we show the
emergence of subdiffusive transport and broad statistics of the local density
of states, suggestive of Griffiths like effects arising from the interplay
between quasiperiodic localization and random coupling to the baths.
Giulio Biroli, Charlotte Rulquin, Gilles Tarjus, Marco Tarzia
SciPost Phys. 1, 007 (2016) ·
published 25 October 2016
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We study the role of fluctuations on the thermodynamic glassy properties of
plaquette spin models, more specifically on the transition involving an overlap
order parameter in the presence of an attractive coupling between different
replicas of the system. We consider both short-range fluctuations associated
with the local environment on Bethe lattices and long-range fluctuations that
distinguish Euclidean from Bethe lattices with the same local environment. We
find that the phase diagram in the temperature-coupling plane is very sensitive
to the former but, at least for the $3$-dimensional (square pyramid) model,
appears qualitatively or semi-quantitatively unchanged by the latter. This
surprising result suggests that the mean-field theory of glasses provides a
reasonable account of the glassy thermodynamics of models otherwise described
in terms of the kinetically constrained motion of localized defects and taken
as a paradigm for the theory of dynamic facilitation. We discuss the possible
implications for the dynamical behavior.
