650 research outputs found
Out of equilibrium correlation functions of quantum anisotropic XY models: one-particle excitations
We calculate exactly matrix elements between states that are not eigenstates
of the quantum XY model for general anisotropy. Such quantities therefore
describe non equilibrium properties of the system; the Hamiltonian does not
contain any time dependence. These matrix elements are expressed as a sum of
Pfaffians. For single particle excitations on the ground state the Pfaffians in
the sum simplify to determinants.Comment: 11 pages, no figures; revtex. Minor changes in the text; list of
refs. modifie
One-Dimensional Impenetrable Anyons in Thermal Equilibrium. II. Determinant Representation for the Dynamic Correlation Functions
We have obtained a determinant representation for the time- and
temperature-dependent field-field correlation function of the impenetrable
Lieb-Liniger gas of anyons through direct summation of the form factors. In the
static case, the obtained results are shown to be equivalent to those that
follow from the anyonic generalization of Lenard's formula.Comment: 16 pages, RevTeX
Mesoscopic BCS pairing in the repulsive 1d-Hubbard model
We study mesoscopic pairing in the one dimensional repulsive Hubbard model
and its interplay with the BCS model in the canonical ensemble. The key tool is
comparing the Bethe ansatz equations of the two models in the limit of small
Coulomb repulsion. For the ordinary Hubbard interaction the BCS Bethe equations
with infinite pairing coupling are recovered; a finite pairing is obtained by
considering a further density-dependent phase-correlation in the hopping
amplitude of the Hubbard model. We find that spin degrees of freedom in the
Hubbard ground state are arranged in a state of the BCS type, where the
Cooper-pairs form an un-condensed liquid on a ``lattice'' of single particle
energies provided by the Hubbard charge degrees of freedom; the condensation in
the BCS ground state corresponds to Hubbard excitations constituted by a sea of
spin singlets.Comment: 15 pages, 6 figures. To be published on Physical Review
Classification of qubit entanglement: SL(2,C) versus SU(2) invariance
The role of SU(2) invariants for the classification of multiparty
entanglement is discussed and exemplified for the Kempe invariant I_5 of pure
three-qubit states. It is found to being an independent invariant only in
presence of both W-type entanglement and threetangle. In this case, constant
I_5 admits for a wide range of both threetangle and concurrences. Furthermore,
the present analysis indicates that an SL^3 orbit of states with equal tangles
but continuously varying I_5 must exist. This means that I_5 provides no
information on the entanglement in the system in addition to that contained in
the tangles (concurrences and threetangle) themselves. Together with the
numerical evidence that I_5 is an entanglement monotone this implies that SU(2)
invariance or the monotone property are too weak requirements for the
characterization and quantification of entanglement for systems of three
qubits, and that SL(2,C) invariance is required. This conclusion can be
extended to general multipartite systems (including higher local dimension)
because the entanglement classes of three-qubit systems appear as subclasses.Comment: 9 pages, 10 figures, revtex
One-Dimensional Impenetrable Anyons in Thermal Equilibrium. IV. Large Time and Distance Asymptotic Behavior of the Correlation Functions
This work presents the derivation of the large time and distance asymptotic
behavior of the field-field correlation functions of impenetrable
one-dimensional anyons at finite temperature. In the appropriate limits of the
statistics parameter, we recover the well-known results for impenetrable bosons
and free fermions. In the low-temperature (usually expected to be the
"conformal") limit, and for all values of the statistics parameter away from
the bosonic point, the leading term in the correlator does not agree with the
prediction of the conformal field theory, and is determined by the singularity
of the density of the single-particle states at the bottom of the
single-particle energy spectrum.Comment: 26 pages, RevTeX
Rescaling multipartite entanglement measures for mixed states
A relevant problem regarding entanglement measures is the following: Given an
arbitrary mixed state, how does a measure for multipartite entanglement change
if general local operations are applied to the state? This question is
nontrivial as the normalization of the states has to be taken into account.
Here we answer it for pure-state entanglement measures which are invariant
under determinant 1 local operations and homogeneous in the state coefficients,
and their convex-roof extension which quantifies mixed-state entanglement. Our
analysis allows to enlarge the set of mixed states for which these important
measures can be calculated exactly. In particular, our results hint at a
distinguished role of entanglement measures which have homogeneous degree 2 in
the state coefficients.Comment: Published version plus one important reference (Ref. [39]
Entanglement and Spontaneous Symmetry Breaking in Quantum Spin Models
It is shown that spontaneous symmetry breaking does not modify the
ground-state entanglement of two spins, as defined by the concurrence, in the
XXZ- and the transverse field Ising-chain. Correlation function inequalities,
valid in any dimensions for these models, are presented outlining the regimes
where entanglement is unaffected by spontaneous symmetry breaking
Entanglement and correlation in anisotropic quantum spin systems
Analytical expressions for the entanglement measures concurrence,
i-concurrence and 3-tangle in terms of spin correlation functions are derived
using general symmetries of the quantum spin system. These relations are
exploited for the one-dimensional XXZ-model, in particular the concurrence and
the critical temperature for disentanglement are calculated for finite systems
with up to six qubits. A recent NMR quantum error correction experiment is
analyzed within the framework of the proposed theoretical approach.Comment: 8 pages, 3 figure
Off-diagonal correlations in one-dimensional anyonic models: A replica approach
We propose a generalization of the replica trick that allows to calculate the
large distance asymptotic of off-diagonal correlation functions in anyonic
models with a proper factorizable ground-state wave-function. We apply this new
method to the exact determination of all the harmonic terms of the correlations
of a gas of impenetrable anyons and to the Calogero Sutherland model. Our
findings are checked against available analytic and numerical results.Comment: 19 pages, 5 figures, typos correcte
Dynamics of Entanglement in One-Dimensional Spin Systems
We study the dynamics of quantum correlations in a class of exactly solvable
Ising-type models. We analyze in particular the time evolution of initial Bell
states created in a fully polarized background and on the ground state. We find
that the pairwise entanglement propagates with a velocity proportional to the
reduced interaction for all the four Bell states. Singlet-like states are
favored during the propagation, in the sense that triplet-like states change
their character during the propagation under certain circumstances.
Characteristic for the anisotropic models is the instantaneous creation of
pairwise entanglement from a fully polarized state; furthermore, the
propagation of pairwise entanglement is suppressed in favor of a creation of
different types of entanglement. The ``entanglement wave'' evolving from a Bell
state on the ground state turns out to be very localized in space-time. Further
support to a recently formulated conjecture on entanglement sharing is given.Comment: 25 pages, 21 figures; revte
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