40 research outputs found
Spatial Kibble-Zurek mechanism through susceptibilities: the inhomogeneous quantum Ising model case
We study the quantum Ising model in the transverse inhomogeneous magnetic
field. Such a system can be approached numerically through exact
diagonalization and analytically through the renormalization group techniques.
Basic insights into its physics, however, can be obtained by adopting the
Kibble-Zurek theory of non-equilibrium phase transitions to description of
spatially inhomogeneous systems at equilibrium. We employ all these approaches
and focus on derivatives of longitudinal and transverse magnetizations, which
have extrema near the critical point. We discuss how these extrema can be used
for locating the critical point and for verification of the Kibble-Zurek
scaling predictions in the spatial quench.Comment: 14 pages, small updates, published versio
Variational Bose-Hubbard model revisited
For strongly interacting bosons in optical lattices the standard description
using Bose-Hubbard model becomes questionable. The role of excited bands
becomes important. In such a situation we compare results of simulations using
multiband Bose-Hubbard model with a recent proposition based on a time
dependent variational approach. It is shown that the latter, in its original
formulation, uses too small variational space leading often to spurious
effects. Possible expansion of variational approach is discussed.Comment: 8 pages, 6 figure
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
Locating the quantum critical point of the Bose-Hubbard model through singularities of simple observables
We show that the critical point of the two-dimensional Bose-Hubbard model can
be easily found through studies of either on-site atom number fluctuations or
the nearest-neighbor two-point correlation function (the expectation value of
the tunnelling operator). Our strategy to locate the critical point is based on
the observation that the derivatives of these observables with respect to the
parameter that drives the superfluid-Mott insulator transition are singular at
the critical point in the thermodynamic limit. Performing the quantum Monte
Carlo simulations of the two-dimensional Bose-Hubbard model, we show that this
technique leads to the accurate determination of the position of its critical
point. Our results can be easily extended to the three-dimensional Bose-Hubbard
model and different Hubbard-like models. They provide a simple
experimentally-relevant way of locating critical points in various cold atomic
lattice systems.Comment: 8 pages, rewritten title, abstract & introductio
Dynamics of heat and mass transport in a quantum insulator
The real time evolution of two pieces of quantum insulators, initially at
different temperatures, is studied when they are glued together. Specifically,
each subsystem is taken as a Bose-Hubbard model in a Mott insulator state. The
process of temperature equilibration via heat transfer is simulated in real
time using the Minimally Entangled Typical Thermal States algorithm. The
analytic theory based on quasiparticles transport is also given.Comment: small clarifying changes, 3 references adde
Random Kronig-Penney-type potentials for ultracold atoms using dark states
A construction of a quasi-random potential for cold atoms using dark states
emerging in {level configuration} is proposed. Speckle laser fields
are used as a source of randomness.
Anderson localisation in such potentials is studied and compared with the
known results for the speckle potential itself. It is found out that the
localisation length is greatly decreased due to the non-linear fashion in which
dark-state potential is obtained. In effect, random dark state potentials
resemble those occurring in random Kronig-Penney-type Hamiltonians.Comment: 12 pages, 8 figure
Random Kronig-Penney-type potentials for ultracold atoms using dark states
A construction of a quasirandom potential for cold atoms using dark states emerging in 螞 level configuration is proposed. Speckle laser fields are used as a source of randomness. Anderson localisation in such potentials is studied and compared with the known results for the speckle potential itself. It is found out that the localization length is greatly decreased due to the nonlinear fashion in which dark-state potential is obtained. In effect, random dark-state potentials resemble those occurring in random Kronig-Penney-type Hamiltonians