SciPost Phys. 11, 074 (2021) ·
published 6 October 2021
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The fully frustrated ladder - a quasi-1D geometrically frustrated spin one
half Heisenberg model - is non-integrable with local conserved quantities on
rungs of the ladder, inducing the fragmentation of the Hilbert space into
sectors composed of singlets and triplets on rungs. We explore the
far-from-equilibrium dynamics of this model through the entanglement entropy
and out-of-time-ordered correlators (OTOC). The post-quench dynamics of the
entanglement entropy is highly anomalous as it shows clear non-damped revivals
that emerge from short connected chunks of triplets and whose persistence is
therefore a consequence of fragmentation. We find that the maximum value of the
entropy follows from a picture where coherences between different fragments
co-exist with perfect thermalization within each fragment. This means that the
eigenstate thermalization hypothesis holds within all sufficiently large
Hilbert space fragments. The OTOC shows short distance oscillations arising
from short coupled fragments, which become decoherent at longer distances, and
a sub-ballistic spreading and long distance exponential decay stemming from an
emergent length scale tied to fragmentation.
Luis Colmenarez, Paul A. McClarty, Masudul Haque, David J. Luitz
SciPost Phys. 7, 064 (2019) ·
published 21 November 2019
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Ergodic quantum many-body systems satisfy the eigenstate thermalization
hypothesis (ETH). However, strong disorder can destroy ergodicity through
many-body localization (MBL) -- at least in one dimensional systems -- leading
to a clear signal of the MBL transition in the probability distributions of
energy eigenstate expectation values of local operators. For a paradigmatic
model of MBL, namely the random-field Heisenberg spin chain, we consider the
full probability distribution of eigenstate correlation functions across the
entire phase diagram. We find gaussian distributions at weak disorder, as
predicted by pure ETH. At intermediate disorder -- in the thermal phase -- we
find further evidence for anomalous thermalization in the form of heavy tails
of the distributions. In the MBL phase, we observe peculiar features of the
correlator distributions: a strong asymmetry in $S_i^z S_{i+r}^z$ correlators
skewed towards negative values; and a multimodal distribution for spin-flip
correlators. A quantitative quasi-degenerate perturbation theory calculation of
these correlators yields a surprising agreement of the full distribution with
the exact results, revealing, in particular, the origin of the multiple peaks
in the spin-flip correlator distribution as arising from the resonant and
off-resonant admixture of spin configurations. The distribution of the
$S_i^zS_{i+r}^z$ correlator exhibits striking differences between the MBL and
Anderson insulator cases.
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