75 research outputs found
Quenching through Dirac and semi-Dirac points in optical Lattices: Kibble-Zurek scaling for anisotropic Quantum-Critical systems
We propose that Kibble-Zurek scaling can be studied in optical lattices by
creating geometries that support, Dirac, Semi-Dirac and Quadratic Band
Crossings. On a Honeycomb lattice with fermions, as a staggered on-site
potential is varied through zero, the system crosses the gapless Dirac points,
and we show that the density of defects created scales as , where
is the inverse rate of change of the potential, in agreement with the
Kibble-Zurek relation. We generalize the result for a passage through a
semi-Dirac point in dimensions, in which spectrum is linear in parallel
directions and quadratic in rest of the perpendicular directions. We
find that the defect density is given by where
and are the dynamical exponents and the correlation
length exponents along the parallel and perpendicular directions, respectively.
The scaling relations are also generalized to the case of non-linear quenching
Quenching across quantum critical points: role of topological patterns
We introduce a one-dimensional version of the Kitaev model consisting of
spins on a two-legged ladder and characterized by Z_2 invariants on the
plaquettes of the ladder. We map the model to a fermionic system and identify
the topological sectors associated with different Z_2 patterns in terms of
fermion occupation numbers. Within these different sectors, we investigate the
effect of a linear quench across a quantum critical point. We study the
dominant behavior of the system by employing a Landau-Zener-type analysis of
the effective Hamiltonian in the low-energy subspace for which the effective
quenching can sometimes be non-linear. We show that the quenching leads to a
residual energy which scales as a power of the quenching rate, and that the
power depends on the topological sectors and their symmetry properties in a
non-trivial way. This behavior is consistent with the general theory of quantum
quenching, but with the correlation length exponent \nu being different in
different sectors.Comment: 5 pages including 2 figures; this is the published versio
Quenching along a gapless line: A different exponent for defect density
We use a new quenching scheme to study the dynamics of a one-dimensional
anisotropic spin-1/2 chain in the presence of a transverse field which
alternates between the values h+\de and h-\de from site to site. In this
quenching scheme, the parameter denoting the anisotropy of interaction (\ga)
is linearly quenched from to as \ga = t/\tau, keeping
the total strength of interaction fixed. The system traverses through a
gapless phase when \ga is quenched along the critical surface h^2 = \de^2 +
J^2 in the parameter space spanned by , \de and \ga. By mapping to an
equivalent two-level Landau-Zener problem, we show that the defect density in
the final state scales as , a behavior that has not been observed
in previous studies of quenching through a gapless phase. We also generalize
the model incorporating additional alternations in the anisotropy or in the
strength of the interaction, and derive an identical result under a similar
quenching. Based on the above results, we propose a general scaling of the
defect density with the quenching rate for quenching along a gapless
critical line.Comment: 6 Pages, 2 figures, accepted in Phys. Rev.
Defect production due to quenching through a multicritical point
We study the generation of defects when a quantum spin system is quenched
through a multicritical point by changing a parameter of the Hamiltonian as
, where is the characteristic time scale of quenching. We argue
that when a quantum system is quenched across a multicritical point, the
density of defects () in the final state is not necessarily given by the
Kibble-Zurek scaling form , where is the
spatial dimension, and and are respectively the correlation length
and dynamical exponent associated with the quantum critical point. We propose a
generalized scaling form of the defect density given by , where the exponent determines the behavior of the
off-diagonal term of the Landau-Zener matrix at the multicritical
point. This scaling is valid not only at a multicritical point but also at an
ordinary critical point.Comment: 4 pages, 2 figures, updated references and added one figur
Defect generation in a spin-1/2 transverse XY chain under repeated quenching of the transverse field
We study the quenching dynamics of a one-dimensional spin-1/2 model in a
transverse field when the transverse field is quenched repeatedly
between and . A single passage from to or the other way around is referred to as a half-period of
quenching. For an even number of half-periods, the transverse field is brought
back to the initial value of ; in the case of an odd number of
half-periods, the dynamics is stopped at . The density of
defects produced due to the non-adiabatic transitions is calculated by mapping
the many-particle system to an equivalent Landau-Zener problem and is generally
found to vary as for large ; however, the magnitude is
found to depend on the number of half-periods of quenching. For two successive
half-periods, the defect density is found to decrease in comparison to a single
half-period, suggesting the existence of a corrective mechanism in the reverse
path. A similar behavior of the density of defects and the local entropy is
observed for repeated quenching. The defect density decays as
for large for any number of half-periods, and shows a increase in kink
density for small for an even number; the entropy shows qualitatively
the same behavior for any number of half-periods. The probability of
non-adiabatic transitions and the local entropy saturate to 1/2 and ,
respectively, for a large number of repeated quenching.Comment: 5 pages, 3 figure
Chopped random-basis quantum optimization
In this work we describe in detail the "Chopped RAndom Basis" (CRAB) optimal
control technique recently introduced to optimize t-DMRG simulations
[arXiv:1003.3750]. Here we study the efficiency of this control technique in
optimizing different quantum processes and we show that in the considered cases
we obtain results equivalent to those obtained via different optimal control
methods while using less resources. We propose the CRAB optimization as a
general and versatile optimal control technique.Comment: 9 pages, 10 figure
Adiabatic multicritical quantum quenches: Continuously varying exponents depending on the direction of quenching
We study adiabatic quantum quenches across a quantum multicritical point
(MCP) using a quenching scheme that enables the system to hit the MCP along
different paths. We show that the power-law scaling of the defect density with
the rate of driving depends non-trivially on the path, i.e., the exponent
varies continuously with the parameter that defines the path, up to a
critical value ; on the other hand for , the scaling exponent saturates to a constant value. We show that
dynamically generated and {\it path()-dependent} effective critical
exponents associated with the quasicritical points lying close to the MCP (on
the ferromagnetic side), where the energy-gap is minimum, lead to this
continuously varying exponent. The scaling relations are established using the
integrable transverse XY spin chain and generalized to a MCP associated with a
-dimensional quantum many-body systems (not reducible to two-level systems)
using adiabatic perturbation theory. We also calculate the effective {\it
path-dependent} dimensional shift (or the shift in center of the
impulse region) that appears in the scaling relation for special paths lying
entirely in the paramagnetic phase. Numerically obtained results are in good
agreement with analytical predictions.Comment: 5 pages, 4 figure
Dynamical delocalization of Majorana edge states by sweeping across a quantum critical point
We study the adiabatic dynamics of Majorana fermions across a quantum phase
transition. We show that the Kibble-Zurek scaling, which describes the density
of bulk defects produced during the critical point crossing, is not valid for
edge Majorana fermions. Therefore, the dynamics governing an edge state quench
is nonuniversal and depends on the topological features of the system. Besides,
we show that the localization of Majorana fermions is a necessary ingredient to
guaranty robustness against defect production.Comment: Submitted to the Special Issue on "Dynamics and Thermalization in
Isolated Quantum Many-Body Systems" in New Journal of Physics. Editors:M.
Cazalilla, M. Rigol. New references and some typos correcte
Quantum Discord in a spin-1/2 transverse XY Chain Following a Quench
We report a study on the zero-temperature quantum discord as a measure of
two-spin correlation of a transverse XY spin chain following a quench across a
quantum critical point and investigate the behavior of mutual information,
classical correlations and hence of discord in the final state as a function of
the rate of quenching. We show that though discord vanishes in the limit of
very slow as well as very fast quenching, it exhibits a peak for an
intermediate value of the quenching rate. We show that though discord and also
the mutual information exhibit a similar behavior with respect to the quenching
rate to that of concurrence or negativity following an identical quenching,
there are quantitative differences. Our studies indicate that like concurrence,
discord also exhibits a power law scaling with the rate of quenching in the
limit of slow quenching though it may not be expressible in a closed power law
form. We also explore the behavior of discord on quenching linearly across a
quantum multicritical point (MCP) and observe a scaling similar to that of the
defect density.Comment: 6 pages, 5 figure
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