21 research outputs found
Density of defects and the scaling law of the entanglement entropy in quantum phase transition of one dimensional spin systems induced by a quench
We have studied quantum phase transition induced by a quench in different one
dimensional spin systems. Our analysis is based on the dynamical mechanism
which envisages nonadiabaticity in the vicinity of the critical point. This
causes spin fluctuation which leads to the random fluctuation of the Berry
phase factor acquired by a spin state when the ground state of the system
evolves in a closed path. The two-point correlation of this phase factor is
associated with the probability of the formation of defects. In this framework,
we have estimated the density of defects produced in several one dimensional
spin chains. At the critical region, the entanglement entropy of a block of
spins with the rest of the system is also estimated which is found to increase
logarithmically with . The dependence on the quench time puts a constraint
on the block size . It is also pointed out that the Lipkin-Meshkov-Glick
model in point-splitting regularized form appears as a combination of the XXX
model and Ising model with magnetic field in the negative z-axis. This unveils
the underlying conformal symmetry at criticality which is lost in the sharp
point limit. Our analysis shows that the density of defects as well as the
scaling behavior of the entanglement entropy follows a universal behavior in
all these systems.Comment: 4 figures, Accepted in Phys. Rev.
Qubit rotation and Berry Phase
A quantized fermion can be represented by a scalar particle encircling a
magnetic flux line. It has the spinor structure which can be constructed from
quantum gates and qubits. We have studied here the role of Berry phase in
removing dynamical phase during one qubit rotation of a quantized fermion. The
entanglement of two qubit inserting spin-echo to one of them results the change
of Berry phase that can be considered as a measure of entanglement. Some effort
is given to study the effect of noise on the Berry phase of spinor and their
entangled states.Comment: 12 page