131 research outputs found
Maximum group velocity in a one-dimensional model with a sinusoidally varying staggered potential
We use Floquet theory to study the maximum value of the stroboscopic group
velocity in a one-dimensional tight-binding model subjected to an on-site
staggered potential varying sinusoidally in time. The results obtained by
numerically diagonalizing the Floquet operator are analyzed using a variety of
analytical schemes. In the low frequency limit we use adiabatic theory, while
in the high frequency limit the Magnus expansion of the Floquet Hamiltonian
turns out to be appropriate. When the magnitude of the staggered potential is
much greater or much less than the hopping, we use degenerate Floquet
perturbation theory; we find that dynamical localization occurs in the former
case when the maximum group velocity vanishes. Finally, starting from an
"engineered" initial state where the particles (taken to be hard core bosons)
are localized in one part of the chain, we demonstrate that the existence of a
maximum stroboscopic group velocity manifests in a light cone like spreading of
the particles in real space.Comment: 8 pages, 5 figures; this is the final published versio
Fidelity, Rosen-Zener Dynamics, Entropy and Decoherence in one dimensional hard-core bosonic systems
We study the non-equilibrium dynamics of a one-dimensional system of hard
core bosons (HCBs) in the presence of an onsite potential (with an alternating
sign between the odd and even sites) which shows a quantum phase transition
(QPT) from the superfluid (SF) phase to the so-called "Mott Insulator" (MI)
phase. The ground state quantum fidelity shows a sharp dip at the quantum
critical point (QCP) while the fidelity susceptibility shows a divergence right
there with its scaling given in terms of the correlation length exponent of the
QPT. We then study the evolution of this bosonic system following a quench in
which the magnitude of the alternating potential is changed starting from zero
(the SF phase) to a non-zero value (the MI phase) according to a half Rosen
Zener (HRZ) scheme or brought back to the initial value following a full Rosen
Zener (FRZ) scheme. The local von Neumann entropy density is calculated in the
final MI phase (following the HRZ quench) and is found to be less than the
equilibrium value () due to the defects generated in the final state as
a result of the quenching starting from the QCP of the system. We also briefly
dwell on the FRZ quenching scheme in which the system is finally in the SF
phase through the intermediate MI phase and calculate the reduction in the
supercurrent and the non-zero value of the residual local entropy density in
the final state. Finally, the loss of coherence of a qubit (globally and weekly
coupled to the HCB system) which is initially in a pure state is investigated
by calculating the time-dependence of the decoherence factor when the HCB chain
evolves under a HRZ scheme starting from the SF phase. This result is compared
with that of the sudden quench limit of the half Rosen-Zener scheme where an
exact analytical form of the decoherence factor can be derived.Comment: To appear in European Physical Journal
Dynamical localization in a chain of hard core bosons under a periodic driving
We study the dynamics of a one-dimensional lattice model of hard core bosons
which is initially in a superfluid phase with a current being induced by
applying a twist at the boundary. Subsequently, the twist is removed and the
system is subjected to periodic \de-function kicks in the staggered on-site
potential. We present analytical expressions for the current and work done in
the limit of an infinite number of kicks. Using these, we show that the current
(work done) exhibit a number of dips (peaks) as a function of the driving
frequency and eventually saturates to zero (a finite value) in the limit of
large frequency. The vanishing of the current (and the saturation of the work
done) can be attributed to a dynamic localization of the hard core bosons
occurring as a consequence of the periodic driving. Remarkably, we show that
for some specific values of the driving amplitude, the localization occurs for
any value of the driving frequency. Moreover, starting from a half-filled
lattice of hard core bosons with the particles localized in the central region,
we show that the spreading of the particles occurs in a light-cone-like region
with a group velocity that vanishes when the system is dynamically localized.Comment: 5 pages, and 3 figures. Accepted for publication in PR
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