273 research outputs found
Discrete disorder models for many-body localization
Using exact diagonalization technique, we investigate the many-body
localization phenomenon in the 1D Heisenberg chain comparing several disorder
models. In particular we consider a family of discrete distributions of
disorder strengths and compare the results with the standard uniform
distribution. Both statistical properties of energy levels and the long time
non-ergodic behavior are discussed. The results for different discrete
distributions are essentially identical to those obtained for the continuous
distribution, provided the disorder strength is rescaled by the standard
deviation of the random distribution. Only for the binary distribution
significant deviations are observed.Comment: version accepted in Phys. Rev.
Properties of the one-dimensional Bose-Hubbard model from a high-order perturbative expansion
We employ a high-order perturbative expansion to characterize the ground
state of the Mott phase of the one-dimensional Bose-Hubbard model. We compute
for different integer filling factors the energy per lattice site, the
two-point and density-density correlations, and expectation values of powers of
the on-site number operator determining the local atom number fluctuations
(variance, skewness, kurtosis). We compare these expansions to numerical
simulations of the infinite-size system to determine their range of
applicability. We also discuss a new sum rule for the density-density
correlations that can be used in both equilibrium and non-equilibrium systems.Comment: 16 pages, published versio
Different lattice geometries with synthetic dimension
The possibility of creating different geometries with the help of an extra
synthetic dimension in optical lattices is studied. Additional linear potential
and Raman assisted tunnelings are used to engineer well controlled tunnelings
between available states. The great flexibility of the system allows us to
obtain different geometries of synthetic lattices with possibility of adding
synthetic gauge fields.Comment: 4pp.
Fast dynamics for atoms in optical lattices
Cold atoms in optical lattices allow for accurate studies of many body
dynamics. Rapid time-dependent modifications of optical lattice potentials may
result in significant excitations in atomic systems. The dynamics in such a
case is frequently quite incompletely described by standard applications of
tight-binding models (such as e.g. Bose-Hubbard model or its extensions) that
typically neglect the effect of the dynamics on the transformation between the
real space and the tight-binding basis. We illustrate the importance of a
proper quantum mechanical description using a multi-band extended Bose-Hubbard
model with time-dependent Wannier functions. We apply it to situations,
directly related to experiments.Comment: 4pp+supplement, final version accepted in Phys. Rev. Let
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
Impact of geometry on many-body localization
The impact of geometry on many body localization is studied on simple,
exemplary systems amenable to exact diagonalization treatment. The crossover
between ergodic and MBL phase for uniform as well as quasi-random disorder is
analyzed using statistics of energy levels. It is observed that the transition
to many-body localized phase is correlated with the number of nearest coupled
neighbors. The crossover from extended to localized systems is approximately
described by the so called plasma model.Comment: 8pp. comments welcom
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 in Bose-Hubbard model: evidence for the mobility edge
Motivated by recent experiments on interacting bosons in
quasi-one-dimensional optical lattice [Nature {\bf 573}, 385 (2019)] we analyse
theoretically properties of the system in the crossover between delocalized and
localized regimes. Comparison of time dynamics for uniform and density wave
like initial states enables demonstration of the existence of the mobility
edge. To this end we define a new observable, the mean speed of transport at
long times. It gives us an efficient estimate of the critical disorder for the
crossover. We also show that the mean velocity growth of occupation
fluctuations close to the edges of the system carries the similar information.
Using the quantum quench procedure we show that it is possible to probe the
mobility edge for different energies.Comment: 4+4pp. major revisio
- …