137 research outputs found
Level statistics across the many--body localization transition
Level statistics of systems that undergo many--body localization transition
are studied. An analysis of the gap ratio statistics from the perspective of
inter- and intra-sample randomness allows us to pin point differences between
transitions in random and quasi-random disorder, showing the effects due to
Griffiths rare events for the former case. It is argued that the transition in
the case of random disorder exhibits universal features that are identified by
constructing an appropriate model of intermediate spectral statistics which is
a generalization of the family of short-range plasma models. The considered
weighted short-range plasma model yields a very good agreement both for level
spacing distribution including its exponential tail and the number variance up
to tens of level spacings outperforming previously proposed models. In
particular, our model grasps the critical level statistics which arise at
disorder strength for which the inter-sample fluctuations are the strongest.
Going beyond the paradigmatic examples of many-body localization in spin
systems, we show that the considered model also grasps the level statistics of
disordered Bose- and Fermi-Hubbard models. The remaining deviations for
long-range spectral correlations are discussed and attributed mainly to the
intricacies of level unfolding.Comment: 19pp. enlarged by including 1807.06983; version accepted in Phys.
Rev.
Many-body localization of bosons in optical lattices
Many-body localization for a system of bosons trapped in a one dimensional
lattice is discussed. Two models that may be realized for cold atoms in optical
lattices are considered. The model with a random on-site potential is compared
with previously introduced random interactions model. While the origin and
character of the disorder in both systems is different they show interesting
similar properties. In particular, many-body localization appears for a
sufficiently large disorder as verified by a time evolution of initial density
wave states as well as using statistical properties of energy levels for small
system sizes. Starting with different initial states, we observe that the
localization properties are energy-dependent which reveals an inverted
many-body localization edge in both systems (that finding is also verified by
statistical analysis of energy spectrum). Moreover, we consider computationally
challenging regime of transition between many body localized and extended
phases where we observe a characteristic algebraic decay of density
correlations which may be attributed to subdiffusion (and Griffiths-like
regions) in the studied systems. Ergodicity breaking in the disordered
Bose-Hubbard models is compared with the slowing-down of the time evolution of
the clean system at large interactions.Comment: expanded second version, comments welcom
Many-body localization due to random interactions
The possibility of observing many body localization of ultracold atoms in a
one dimensional optical lattice is discussed for random interactions. In the
non-interacting limit, such a system reduces to single-particle physics in the
absence of disorder, i.e. to extended states. In effect the observed
localization is inherently due to interactions and is thus a genuine many-body
effect. In the system studied, many-body localization manifests itself in a
lack of thermalization visible in temporal propagation of a specially prepared
initial state, in transport properties, in the logarithmic growth of
entanglement entropy as well as in statistical properties of energy levels.Comment: 5pp, 4figs. version close to published on
Energy level dynamics across the many-body localization transition
The level dynamics across the many body localization transition is examined
for XXZ-spin model with a random magnetic field. We compare different scenaria
of parameter dependent motion in the system and consider measures such as level
velocities, curvatures as well as their fidelity susceptibilities. Studying the
ergodic phase of the model we find that the level dynamics does not reveal the
commonly believed universal behavior after rescaling the curvatures by the
level velocity variance. At the same time, distributions of level curvatures
and fidelity susceptibilities coincide with properly rescaled distributions for
Gaussian Orthogonal Ensemble of random matrices. Profound differences exists
depending on way the level dynamics is imposed in the many-body localized phase
of the model in which the level dynamics can be understood with the help of
local integrals of motion.Comment: version close to that accepted in PR
Polynomially filtered exact diagonalization approach to many-body localization
Polynomially filtered exact diagonalization method (POLFED) for large sparse
matrices is introduced. The algorithm finds an optimal basis of a subspace
spanned by eigenvectors with eigenvalues close to a specified energy target by
a spectral transformation using a high order polynomial of the matrix. The
memory requirements scale better with system size than in the state-of-the-art
shift-invert approach. The potential of POLFED is demonstrated examining
many-body localization transition in 1D interacting quantum spin-1/2 chains. We
investigate the disorder strength and system size scaling of Thouless time.
System size dependence of bipartite entanglement entropy and of the gap ratio
highlights the importance of finite-size effects in the system. We discuss
possible scenarios regarding the many-body localization transition obtaining
estimates for the critical disorder strength.Comment: 4+5 pages, version accepted in Physical Review Letters, comments
welcom
Thouless time analysis of Anderson and many-body localization transitions
Spectral statistics of disordered systems encode Thouless and Heisenberg time
scales whose ratio determines whether the system is chaotic or localized.
Identifying similarities between system size and disorder strength scaling of
Thouless time for disordered quantum many-body systems with results for 3D and
5D Anderson models, we argue that the two-parameter scaling breaks down in the
vicinity of the transition to the localized phase signalling subdiffusive
dynamics.Comment: 2nd version, several minor changes in text and discussions expanded,
4+1 pages, 3+1 figures, comments welcom
On two consequences of CH established by Sierpi\'nski
We study the relations between two consequences of the Continuum Hypothesis
discovered by Wac{\l}aw Sierpi\'nski, concerning uniform continuity of
continuous functions and uniform convergence of sequences of real-valued
functions, defined on subsets of the real line of cardinality continuum
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