27 research outputs found
Generalized mean field description of entanglement in dimerized spin systems
We discuss a generalized self-consistent mean field (MF) treatment, based on
the selection of an arbitrary subset of operators for representing the system
density matrix, and its application to the problem of entanglement evaluation
in composite quantum systems. As a specific example, we examine in detail a
pair MF approach to the ground state (GS) of dimerized spin 1/2 systems with
anisotropic ferromagnetic-type XY and XYZ couplings in a transverse field,
including chains and arrays with first neighbor and also longer range
couplings. The approach is fully analytic and able to capture the main features
of the GS of these systems, in contrast with the conventional single spin MF.
Its phase diagram differs significantly from that of the latter, exhibiting
(Sz) parity breaking just in a finite field window if the coupling between
pairs is sufficiently weak, together with a fully dimerized phase below this
window and a partially aligned phase above it. It is then shown that through
symmetry restoration, the approach is able to correctly predict not only the
concurrence of a pair, but also its entanglement with the rest of the chain,
which shows a pronounced peak in the parity breaking window. Perturbative
corrections allow to reproduce more subtle observables like the entanglement
between weakly coupled spins and the low lying energy spectrum. All predictions
are tested against exact results for finite systems.Comment: 13 pages, 9 figures. Final versio
History states of one-dimensional quantum walks
We analyze the application of the history state formalism to quantum walks.
The formalism allows one to describe the whole walk through a pure quantum
history state, which can be derived from a timeless eigenvalue equation. It
naturally leads to the notion of system-time entanglement of the walk, which
can be considered as a measure of the number of orthogonal states visited in
the walk. We then focus on one-dimensional discrete quantum walks, where it is
shown that such entanglement is independent of the initial spin orientation for
real Hadamard-type quantum coins and real initial states (in the standard
basis) with definite site-parity. Moreover, in the case of an initially
localized particle it can be identified with the entanglement of the unitary
global operator that generates the whole history state, which is related to its
entangling power and can be analytically evaluated. Besides, it is shown that
the evolution of the spin subsystem can also be described through a spin
history state with an extended clock. A connection between its average
entanglement (over all initial states) and that of the operator generating this
state is also derived. A quantum circuit for generating the quantum walk
history state is as well provided.Comment: 12 pages, 7 figure