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.
SciPost Phys. Core 5, 023 (2022) ·
published 21 April 2022
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We explore the dynamical phases of unitary Clifford circuits with
variable-range interactions, coupled to a monitoring environment. We
investigate two classes of models, distinguished by the action of the unitary
gates, which either are organized in clusters of finite-range two-body gates,
or are pair-wise interactions randomly distributed throughout the system with a
power-law distribution. We find the range of the interactions plays a key role
in characterizing both phases and their measurement-induced transitions. For
the cluster unitary gates we find a transition between a phase with volume-law
scaling of the entanglement entropy and a phase with area-law entanglement
entropy. Our results indicate that the universality class of the phase
transition is compatible to that of short range hybrid Clifford circuits.
Oppositely, in the case of power-law distributed gates, we find the
universality class of the phase transition changes continuously with the
parameter controlling the range of interactions. In particular, for
intermediate values of the control parameter, we find a non-conformal critical
line which separates a phase with volume-law scaling of the entanglement
entropy from one with sub-extensive scaling. Within this region, we find the
entanglement entropy and the logarithmic negativity present a cross-over from a
phase with algebraic growth of entanglement with system size, and an area-law
phase.
SciPost Phys. 8, 042 (2020) ·
published 16 March 2020
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Variational wave functions have been a successful tool to investigate the
properties of quantum spin liquids. Finding their parent Hamiltonians is of
primary interest for the experimental simulation of these strongly correlated
phases, and for gathering additional insights on their stability. In this work,
we systematically reconstruct approximate spin-chain parent Hamiltonians for
Jastrow-Gutzwiller wave functions, which share several features with quantum
spin liquid wave-functions in two dimensions. Firstly, we determine the
different phases encoded in the parameter space through their correlation
functions and entanglement content. Secondly, we apply a recently proposed
entanglement-guided method to reconstruct parent Hamiltonians to these states,
which constrains the search to operators describing relativistic low-energy
field theories - as expected for deconfined phases of gauge theories relevant
to quantum spin liquids. The quality of the results is discussed using
different quantities and comparing to exactly known parent Hamiltonians at
specific points in parameter space. Our findings provide guiding principles for
experimental Hamiltonian engineering of this class of states.