504 research outputs found
Decoherence in a scalable adiabatic quantum computer
We consider the effects of decoherence on Landau-Zener crossings encountered
in a large-scale adiabatic-quantum-computing setup. We analyze the dependence
of the success probability, i.e. the probability for the system to end up in
its new ground state, on the noise amplitude and correlation time. We determine
the optimal sweep rate that is required to maximize the success probability. We
then discuss the scaling of decoherence effects with increasing system size. We
find that those effects can be important for large systems, even if they are
small for each of the small building blocks.Comment: 6 pages (two-column), 1 figur
Spin Chains as Perfect Quantum State Mirrors
Quantum information transfer is an important part of quantum information
processing. Several proposals for quantum information transfer along linear
arrays of nearest-neighbor coupled qubits or spins were made recently. Perfect
transfer was shown to exist in two models with specifically designed strongly
inhomogeneous couplings. We show that perfect transfer occurs in an entire
class of chains, including systems whose nearest-neighbor couplings vary only
weakly along the chain. The key to these observations is the Jordan-Wigner
mapping of spins to noninteracting lattice fermions which display perfectly
periodic dynamics if the single-particle energy spectrum is appropriate. After
a half-period of that dynamics any state is transformed into its mirror image
with respect to the center of the chain. The absence of fermion interactions
preserves these features at arbitrary temperature and allows for the transfer
of nontrivially entangled states of several spins or qubits.Comment: Abstract extended, introduction shortened, some clarifications in the
text, one new reference. Accepted by Phys. Rev. A (Rapid Communications
Impurity spin relaxation in S=1/2 XX chains
Dynamic autocorrelations (\alpha=x,z) of an
isolated impurity spin in a S=1/2 XX chain are calculated. The impurity spin,
defined by a local change in the nearest-neighbor coupling, is either in the
bulk or at the boundary of the open-ended chain. The exact numerical
calculation of the correlations employs the Jordan-Wigner mapping from spin
operators to Fermi operators; effects of finite system size can be eliminated.
Two distinct temperature regimes are observed in the long-time asymptotic
behavior. At T=0 only power laws are present. At high T the x correlation
decays exponentially (except at short times) while the z correlation still
shows an asymptotic power law (different from the one at T=0) after an
intermediate exponential phase. The boundary impurity correlations follow power
laws at all T. The power laws for the z correlation and the boundary
correlations can be deduced from the impurity-induced changes in the properties
of the Jordan-Wigner fermion states.Comment: Final version to be published in Phys. Rev. B. Three references
added, extended discussion of relation to previous wor
Dynamic properties of quantum spin chains: Simple route to complex behavior
We examine dynamic structure factors of spin-1/2 chains with nearest-neighbor
interactions of XX and Dzyaloshinskii-Moriya type, and with periodic and random
changes in the sign of these interactions. This special kind of inhomogeneity
can be eliminated from the Hamiltonian by suitable transformation of the spin
variables. As a result, the dynamic structure factors of periodic or random
chains can be computed from those of the uniform chains. Using the exact
analytical and precise numerical results available for the uniform systems we
illustrate the effects of regular alternation or random disorder on dynamic
structure factors of quantum spin chains
Efficient and perfect state transfer in quantum chains
We present a communication protocol for chains of permanently coupled qubits
which achieves perfect quantum state transfer and which is efficient with
respect to the number chains employed in the scheme. The system consists of
uncoupled identical quantum chains. Local control (gates, measurements) is only
allowed at the sending/receiving end of the chains. Under a quite general
hypothesis on the interaction Hamiltonian of the qubits a theorem is proved
which shows that the receiver is able to asymptotically recover the messages by
repetitive monitoring of his qubits.Comment: 6 pages, 2 figures; new material adde
Charge and spin dynamics in the one-dimensional and models
The impact of the spin-flip terms on the (static and dynamic) charge and spin
correlations in the Luttinger-liquid ground state of the 1D model is
assessed by comparison with the same quantities in the 1D model, where
spin-flip terms are absent. We employ the recursion method combined with a
weak-coupling or a strong-coupling continued-fraction analysis. At
we use the Pfaffian representation of dynamic spin correlations. The changing
nature of the dynamically relevant charge and spin excitations on approach of
the transition to phase separation is investigated in detail. The
charge excitations (but not the spin excitations) at the transition have a
single-mode nature, whereas charge and spin excitations have a complicated
structure in the model. In the model, phase separation is
accompanied by N\'eel long-range order, caused by the condensation of electron
clusters with an already existing alternating up-down spin configuration
(topological long-range order). In the model, by contrast, the spin-flip
processes in the exchange coupling are responsible for continued strong spin
fluctuations (dominated by 2-spinon excitations) in the phase-separated state.Comment: 11 pages (RevTex). 14 Figures available from author
The Mott-Hubbard Transition on the D=infinity Bethe Lattice
In view of a recent controversy we investigated the Mott-Hubbard transition
in D=infinity with a novel cluster approach. i) We show that any truncated
Bethe lattice of order n can be mapped exactly to a finite Hubbard-like
cluster. ii) We evaluate the self-energy numerically for n=0,1,2 and compare
with a series of self-consistent equation-of-motion solutions. iii) We find the
gap to open continously at the critical U_c~2.5t* (t = t* / sqrt{4d}). iv) A
low-energy theory for the Mott-Hubbard transition is developed and relations
between critical exponents are presented.Comment: Replaced with the published versio
Dynamics of spin correlations in the spin-1/2 isotropic XY chain in a transverse field
Dynamic xx spin pair correlation functions for the isotropic spin-1/2 XY
chain are calculated numerically for long open chains in the presence of a
transverse magnetic field at finite temperature. As an application we discuss
the temperature dependence of the spin-spin relaxation time in PrCl_3.Comment: 2 pages, latex, 2 figures, abstract of the paper presented at Ampere
Summer School ``Applications of Magnetic Resonance in Novel Materials''
Nafplion, Greece, 3-9 September, 2000, partially published in J. Phys. A:
Math. Gen. 33, 3063 (2000
Long-Time Tails and Anomalous Slowing Down in the Relaxation of Spatially Inhomogeneous Excitations in Quantum Spin Chains
Exact analytic calculations in spin-1/2 XY chains, show the presence of
long-time tails in the asymptotic dynamics of spatially inhomogeneous
excitations. The decay of inhomogeneities, for , is given in the
form of a power law where the relaxation time
and the exponent depend on the wave vector ,
characterizing the spatial modulation of the initial excitation. We consider
several variants of the XY model (dimerized, with staggered magnetic field,
with bond alternation, and with isotropic and uniform interactions), that are
grouped into two families, whether the energy spectrum has a gap or not. Once
the initial condition is given, the non-equilibrium problem for the
magnetization is solved in closed form, without any other assumption. The
long-time behavior for can be obtained systematically in a form
of an asymptotic series through the stationary phase method. We found that
gapped models show critical behavior with respect to , in the sense that
there exist critical values , where the relaxation time
diverges and the exponent changes discontinuously. At those points, a
slowing down of the relaxation process is induced, similarly to phenomena
occurring near phase transitions. Long-lived excitations are identified as
incommensurate spin density waves that emerge in systems undergoing the Peierls
transition. In contrast, gapless models do not present the above anomalies as a
function of the wave vector .Comment: 25 pages, 2 postscript figures. Manuscript submitted to Physical
Review
New Results for the Correlation Functions of the Ising Model and the Transverse Ising Chain
In this paper we show how an infinite system of coupled Toda-type nonlinear
differential equations derived by one of us can be used efficiently to
calculate the time-dependent pair-correlations in the Ising chain in a
transverse field. The results are seen to match extremely well long large-time
asymptotic expansions newly derived here. For our initial conditions we use new
long asymptotic expansions for the equal-time pair correlation functions of the
transverse Ising chain, extending an old result of T.T. Wu for the 2d Ising
model. Using this one can also study the equal-time wavevector-dependent
correlation function of the quantum chain, a.k.a. the q-dependent diagonal
susceptibility in the 2d Ising model, in great detail with very little
computational effort.Comment: LaTeX 2e, 31 pages, 8 figures (16 eps files). vs2: Two references
added and minor changes of style. vs3: Corrections made and reference adde
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