197 research outputs found
A constructive theory of the numerically accessible many-body localized to thermal crossover
The many-body localised (MBL) to thermal crossover observed in exact
diagonalisation studies remains poorly understood as the accessible system
sizes are too small to be in an asymptotic scaling regime. We develop a model
of the crossover in short 1D chains in which the MBL phase is destabilised by
the formation of many-body resonances. The model reproduces several properties
of the numerically observed crossover, including an apparent correlation length
exponent , exponential growth of the Thouless time with disorder
strength, linear drift of the critical disorder strength with system size,
scale-free resonances, apparent dependence of disorder-averaged
spectral functions, and sub-thermal entanglement entropy of small subsystems.
In the crossover, resonances induced by a local perturbation are rare at
numerically accessible system sizes which are smaller than a
\emph{resonance length} . For , resonances
typically overlap, and this model does not describe the asymptotic transition.
The model further reproduces controversial numerical observations which Refs.
[\v{S}untajs et al, 2019] and [Sels & Polkovnikov, 2020] claimed to be
inconsistent with MBL. We thus argue that the numerics to date is consistent
with a MBL phase in the thermodynamic limit.Comment: 27 pages, 12 figure
Mean field theory of failed thermalizing avalanches
We show that localization in quasiperiodically modulated, two-dimensional
systems is stable to the presence of a finite density of ergodic grains. This
contrasts with the case of randomly modulated systems, where such grains seed
thermalizing avalanches. These results are obtained within a quantitatively
accurate, self-consistent entanglement mean field theory which analytically
describes two level systems connected to a central ergodic grain. The theory
predicts the distribution of entanglement entropies of each two level system
across eigenstates, and the late time values of dynamical observables. In
addition to recovering the known phenomenology of avalanches, the theory
reproduces exact diagonalization data, and predicts the spatial profile of the
thermalized region when the avalanche fails.Comment: 13 pages, 5 figure
Avalanche induced co-existing localised and thermal regions in disordered chains
We investigate the stability of an Anderson localized chain to the inclusion
of a single finite interacting thermal seed. This system models the effects of
rare low-disorder regions on many-body localized chains. Above a threshold
value of the mean localization length, the seed causes runaway thermalization
in which a finite fraction of the orbitals are absorbed into a thermal bubble.
This `partially avalanched' regime provides a simple example of a delocalized,
non-ergodic dynamical phase. We derive the hierarchy of length scales necessary
for typical samples to exhibit the avalanche instability, and show that the
required seed size diverges at the avalanche threshold. We introduce a new
dimensionless statistic that measures the effective size of the thermal bubble,
and use it to numerically confirm the predictions of avalanche theory in the
Anderson chain at infinite temperature.Comment: 26 pages, 18 figure
Strategies for enhancing quantum entanglement by local photon subtraction
Subtracting photons from a two-mode squeezed state is a well-known method to
increase entanglement. We analyse different strategies of local photon
subtraction from a two-mode squeezed state in terms of entanglement gain and
success probability. We develop a general framework that incorporates
imperfections and losses in all stages of the process: before, during, and
after subtraction. By combining all three effects into a single efficiency
parameter, we provide analytical and numerical results for subtraction
strategies using photon-number-resolving and threshold detectors. We compare
the entanglement gain afforded by symmetric and asymmetric subtraction
scenarios across the two modes. For a given amount of loss, we identify an
optimised set of parameters, such as initial squeezing and subtraction beam
splitter transmissivity, that maximise the entanglement gain rate. We identify
regimes for which asymmetric subtraction of different Fock states on the two
modes outperforms symmetric strategies. In the lossless limit, subtracting a
single photon from one mode always produces the highest entanglement gain rate.
In the lossy case, the optimal strategy depends strongly on the losses on each
mode individually, such that there is no general optimal strategy. Rather,
taking losses on each mode as the only input parameters, we can identify the
optimal subtraction strategy and required beam splitter transmissivities and
initial squeezing parameter. Finally, we discuss the implications of our
results for the distillation of continuous-variable quantum entanglement.Comment: 13 pages, 11 figures. Updated version for publicatio
Pfaffian-like ground states for bosonic atoms and molecules in one-dimensional optical lattices
We study ground states and elementary excitations of a system of bosonic
atoms and diatomic Feshbach molecules trapped in a one-dimensional optical
lattice using exact diagonalization and variational Monte Carlo methods. We
primarily study the case of an average filling of one boson per site. In
agreement with bosonization theory, we show that the ground state of the system
in the thermodynamic limit corresponds to the Pfaffian-like state when the
system is tuned towards the superfluid-to-Mott insulator quantum phase
transition. Our study clarifies the possibility of the creation of exotic
Pfaffian-like states in realistic one-dimensional systems. We also present
preliminary evidence that such states support non-Abelian anyonic excitations
that have potential application for fault-tolerant topological quantum
computation.Comment: 10 pages, 10 figures. Matching the version published Phys.Rev.
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