38 research outputs found
Sudden quenches in quasiperiodic Ising model
We present here the non-equilibrium dynamics of the recently studied
quasiperiodic Ising model. The zero temperature phase diagram of this model
mainly consists of three phases, where each of these three phases can have
extended, localized or critically delocalized low energy excited states. We
explore the nature of excitations in these different phases by studying the
evolution of entanglement entropy after performing quenches of different
strengths to different phases. Our results on non-equilibrium dynamics of
entanglement entropy are concurrent with the nature of excitations discussed in
Ref. 1 in each phase.Comment: 5 pages, 4 figure
Effect of double local quenches on Loschmidt echo and entanglement entropy of a one-dimensional quantum system
We study the effect of two simultaneous local quenches on the evolution of
Loschmidt echo and entanglement entropy of a one dimensional transverse Ising
model. In this work, one of the local quenches involves the connection of two
spin-1/2 chains at a certain time and the other local quench corresponds to a
sudden change in the magnitude of the transverse field at a given site in one
of the spin chains. We numerically calculate the dynamics associated with the
Loschmidt echo and the entanglement entropy as a result of such double
quenches, and discuss various timescales involved in this problem using the
picture of quasiparticles generated as a result of such quenches.Comment: 11 pages, 10 figure
Fidelity susceptibility and Loschmidt echo for generic paths in a three spin interacting transverse Ising model
We study the effect of presence of different types of critical points such as
ordinary critical point, multicritical point and quasicritical point along
different paths on the Fidelity susceptibility and Loschmidt echo of a three
spin interacting transverse Ising chain using a method which does not involve
the language of tensors. We find that the scaling of fidelity susceptibility
and Loschmidt echo with the system size at these special critical points of the
model studied, is in agreement with the known results, thus supporting our
method.Comment: 5 figure
Critical behaviour of mixed random fibers, fibers on a chain and random graph
We study random fiber bundle model (RFBM) with different threshold strength
distributions and load sharing rules. A mixed RFBM within global load sharing
scheme is introduced which consists of weak and strong fibers with uniform
distribution of threshold strength of fibers having a discontinuity. The
dependence of the critical stress of the above model on the measure of the
discontinuity of the distribution is extensively studied. A similar RFBM with
two types of fibers belonging to two different Weibull distribution of
threshold strength is also studied. The variation of the critical stress of a
one dimensional RFBM with the number of fibers is obtained for strictly uniform
distribution and local load sharing using an exact method which assumes
one-sided load transfer. The critical behaviour of RFBM with fibers placed on a
random graph having co-ordination number 3 is investigated numerically for
uniformly distributed threshold strength of fibers subjected to local load
sharing rule, and mean field critical behaviour is established.Comment: graphs included in Section II and III with more detail
The effect of the three-spin interaction and the next-nearest neighbor interaction on the quenching dynamics of a transverse Ising model
We study the zero temperature quenching dynamics of various extensions of the
transverse Ising model (TIM) when the transverse field is linearly quenched
from to (or zero) at a finite and uniform rate. The rate of
quenching is dictated by a characteristic scale given by . The density of
kinks produced in these extended models while crossing the quantum critical
points during the quenching process is calculated using a many body
generalization of the Landau-Zener transition theory. The density of kinks in
the final state is found to decay as . In the first model
considered here, the transverse Ising Hamiltonian includes an additional
ferromagnetic three spin interaction term of strength . For , the
kink density is found to increase monotonically with whereas it decreases
with for . The point and the transverse field
is multicritical where the density shows a slower decay given by
. We also study the effect of ferromagnetic or antiferromagnetic
next nearest neighbor (NNN) interactions on the dynamics of TIM under the same
quenching scheme. In a mean field approximation, the transverse Ising
Hamiltonians with NNN interactions are identical to the three spin Hamiltonian.
The NNN interactions non-trivially modifies the dynamical behavior, for example
an antiferromagnetic NNN interactions results to a larger number of kinks in
the final state in comparison to the case when the NNN interaction is
ferromagnetic.Comment: 7 pages, 4 figure
Tuning the presence of dynamical phase transitions in a generalized spin chain
We study an integrable spin chain with three spin interactions and the
staggered field () while the latter is quenched either slowly (in a
linear fashion in time () as where goes from a large negative
value to a large positive value and is the inverse rate of quenching) or
suddenly. In the process, the system crosses quantum critical points and
gapless phases. We address the question whether there exist non-analyticities
(known as dynamical phase transitions (DPTs)) in the subsequent real time
evolution of the state (reached following the quench) governed by the final
time-independent Hamiltonian. In the case of sufficiently slow quenching (when
exceeds a critical value ), we show that DPTs, of the form
similar to those occurring for quenching across an isolated critical point, can
occur even when the system is slowly driven across more than one critical point
and gapless phases. More interestingly, in the anisotropic situation we show
that DPTs can completely disappear for some values of the anisotropy term
() and , thereby establishing the existence of boundaries in the
plane between the DPT and no-DPT regions in both isotropic and
anisotropic cases. Our study therefore leads to a unique situation when DPTs
may not occur even when an integrable model is slowly ramped across a QCP. On
the other hand, considering sudden quenches from an initial value
to a final value , we show that the condition for the presence of
DPTs is governed by relations involving , and
and the spin chain must be swept across for DPTs to occur.Comment: 8 pages, 5 figure
The three site interacting spin chain in staggered field: Fidelity vs Loschmidt echo
We study the the ground state fidelity and the ground state Loschmidt echo of
a three site interacting XX chain in presence of a staggered field which
exhibits special types of quantum phase transitions due to change in the
topology of the Fermi surface, apart from quantum phase transitions from gapped
to gapless phases. We find that on one hand, the fidelity is able to detect
only the boundaries separating the gapped from the gapless phase; it is
completely insensitive to the phase transition from two Fermi points region to
four Fermi points region lying within this gapless phase. On the other hand,
Loschmidt echo shows a dip only at a special point in the entire phase diagram
and hence fails to detect any quantum phase transition associated with the
present model. We provide appropriate arguments in support of this anomalous
behavior.Comment: 7 pages, 4 Figures, Accepted in Phys. Rev.
Non-equilibrium quantum dynamics after local quenches
We study the quantum dynamics resulting from preparing a one-dimensional
quantum system in the ground state of initially two decoupled parts which are
then joined together (local quench). Specifically we focus on the transverse
Ising chain and compute the time-dependence of the magnetization profile,
m_l(t), and correlation functions at the critical point, in the
ferromagnetically ordered phase and in the paramagnetic phase. At the critical
point we find finite size scaling forms for the nonequilibrium magnetization
and compare predictions of conformal field theory with our numerical results.
In the ferromagnetic phase the magnetization profiles are well matched by our
predictions from a quasi-classical calculation.Comment: 23 pages, 14 figure
Non-equilibrium quantum relaxation across a localization-delocalization transition
We consider the one-dimensional -model in a quasi-periodic
transverse-field described by the Harper potential, which is equivalent to a
tight-binding model of spinless fermions with a quasi-periodic chemical
potential. For weak transverse field (chemical potential), , the
excitations (fermions) are delocalized, but become localized for . We
study the non-equilibrium relaxation of the system by applying two protocols: a
sudden change of (quench dynamics) and a slow change of in time
(adiabatic dynamics). For a quench into the delocalized (localized) phase, the
entanglement entropy grows linearly (saturates) and the order parameter
decreases exponentially (has a finite limiting value). For a critical quench
the entropy increases algebraically with time, whereas the order parameter
decreases with a stretched-exponential. The density of defects after an
adiabatic field change through the critical point is shown to scale with a
power of the rate of field change and a scaling relation for the exponent is
derived.Comment: 10 pages, 6 figures, published versio
Adiabatic dynamics of quasiperiodic transverse Ising model
We study the non-equilibrium dynamics due to slowly taking a quasiperiodic
Hamiltonian across its quantum critical point. The special quasiperiodic
Hamiltonian that we study here has two different types of critical lines
belonging to two different universality classes, one of them being the well
known quantum Ising universality class. In this paper, we verify the Kibble
Zurek scaling which predicts a power law scaling of the density of defects
generated as a function of the rate of variation of the Hamiltonian. The
exponent of this power law is related to the equilibrium critical exponents
associated with the critical point crossed. We show that the power-law behavior
is indeed obeyed when the two types of critical lines are crossed, with the
exponents that are correctly predicted by Kibble Zurek scaling.Comment: 5 pages, 3 figure