7 research outputs found
Critical points of the three-dimensional Bose-Hubbard model from on-site atom number fluctuations
We discuss how positions of critical points of the three-dimensional
Bose-Hubbard model can be accurately obtained from variance of the on-site atom
number operator, which can be experimentally measured. The idea that we explore
is that the derivative of the variance, with respect to the parameter driving
the transition, has a pronounced maximum close to critical points. We show that
Quantum Monte Carlo studies of this maximum lead to precise determination of
critical points for the superfluid-Mott insulator transition in systems with
mean number of atoms per lattice site equal to one, two, and three. We also
extract from such data the correlation-length critical exponent through the
finite-size scaling analysis and discuss how the derivative of the variance can
be reliably computed from numerical data for the variance. The same conclusions
apply to the derivative of the nearest-neighbor correlation function, which can
be obtained from routinely measured time-of-flight images.Comment: 15 pages, corrected typos, updated references, improvements in
discussio
Long persistence of localization in a disordered anharmonic chain beyond the atomic limit
We establish rigorous bounds on dissipative transport in the disordered
Klein-Gordon chain with quartic on-site potential, governed by a parameter
. At , the chain is harmonic and transport is fully
suppressed by Anderson localization. For the anharmonic system at , our results show that dissipative effects set in on time scales that grow
faster than any polynomial in , as . From a technical
perspective, the main novelty of our work is that we do not restrict ourselves
to the atomic limit, i.e. we develop perturbation theory around the harmonic
system with a fixed hopping strength between near oscillators. This allows us
to compare our mathematical results with previous numerical work and contribute
to the resolution of an ongoing debate in the physics community, as we explain
in a companion paper arXiv:2308.10572
Slow dissipation and spreading in disordered classical systems: A direct comparison between numerics and mathematical bounds
We study the breakdown of Anderson localization in the one-dimensional
nonlinear Klein-Gordon chain, a prototypical example of a disordered classical
many-body system. A series of numerical works indicate that an initially
localized wave packet spreads polynomially in time, while analytical studies
rather suggest a much slower spreading. Here, we focus on the decorrelation
time in equilibrium. On the one hand, we provide a mathematical theorem
establishing that this time is larger than any inverse power law in the
effective anharmonicity parameter , and on the other hand our numerics
show that it follows a power law for a broad range of values of . This
numerical behavior is fully consistent with the power law observed numerically
in spreading experiments, and we conclude that the state-of-the-art numerics
may well be unable to capture the long-time behavior of such classical
disordered systems
Rigorous and simple results on very slow thermalization, or quasi-localization, of the disordered quantum chain
This paper originates from lectures delivered at the summer school
"Fundamental Problems in Statistical Physics XV" in Bruneck, Italy, in 2021. We
give a brief and limited introduction into ergodicity-breaking induced by
disorder. As the title suggests, we include a simple yet rigorous and original
result: For a strongly disordered quantum chain, we exhibit a full set of
quasi-local quantities whose dynamics is negligible up to times of order
, with , a numerical
constant, and the disorder strength. Such a result, that is often referred
to as "quasi-localization", can in principle be obtained in other systems as
well, but for a disordered quantum chain, its proof is relatively short and
transparent.Comment: To be published in Physica A: Statistical Mechanics and its
Application
Rigorous and simple results on very slow thermalization, or quasi-localization, of the disordered quantum chain
This paper originates from lectures delivered at the summer school “Fundamental Problems in Statistical Physics XV” in Bruneck, Italy, in 2021. We give a brief and limited introduction into ergodicity-breaking induced by disorder. As the title suggests, we include a simple yet rigorous and original result: For a strongly disordered quantum chain, we exhibit a full set of quasi-local quantities whose dynamics is negligible up to times of order exp{c(logW)2−ϵ}, with ϵ<1, c a numerical constant, and W the disorder strength. Such a result, that is often referred to as “quasi-localization”, can in principle be obtained in other systems as well, but for a disordered quantum chain, its proof is relatively short and transparent.</p