686 research outputs found
Dynamics of quantum spin chains and multi-fermion excitation continua
We use the Jordan-Wigner representation to study dynamic quantities for the
spin-1/2 XX chain in a transverse magnetic field. We discuss in some detail the
properties of the four-fermion excitation continuum which is probed by the
dynamic trimer structure factor.Comment: Presented at the SCES '05 - The International Conference on Strongly
Correlated Electron Systems (Vienna, July 26-30, 2005
COMPLETE SOLUTION OF THE XXZ-MODEL ON FINITE RINGS. DYNAMICAL STRUCTURE FACTORS AT ZERO TEMPERATURE.
The finite size effects of the dynamical structure factors in the XXZ-model
are studied in the euclidean time -representation. Away from the
critical momentum finite size effects turn out to be small except for
the large limit. The large finite size effects at the critical momentum
signal the emergence of infrared singularities in the spectral
-representation of the dynamical structure factors.Comment: PostScript file with 12 pages + 11 figures uuencoded compresse
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
Geometric Effects and Computation in Spin Networks
When initially introduced, a Hamiltonian that realises perfect transfer of a
quantum state was found to be analogous to an x-rotation of a large spin. In
this paper we extend the analogy further to demonstrate geometric effects by
performing rotations on the spin. Such effects can be used to determine
properties of the chain, such as its length, in a robust manner. Alternatively,
they can form the basis of a spin network quantum computer. We demonstrate a
universal set of gates in such a system by both dynamical and geometrical
means
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
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
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
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
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