1,047 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
Scaling of Entanglement Entropy in the Random Singlet Phase
We present numerical evidences for the logarithmic scaling of the
entanglement entropy in critical random spin chains. Very large scale exact
diagonalizations performed at the critical XX point up to L=2000 spins 1/2 lead
to a perfect agreement with recent real-space renormalization-group predictions
of Refael and Moore [Phys. Rev. Lett. {\bf 93}, 260602 (2004)] for the
logarithmic scaling of the entanglement entropy in the Random Singlet Phase
with an effective central charge . Moreover we
provide the first visual proof of the existence the Random Singlet Phase thanks
to the quantum entanglement concept.Comment: 4 pages, 3 figure
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
Quantum many particle systems in ring-shaped optical lattices
In the present work we demonstrate how to realize 1d-optical closed lattice
experimentally, including a {\it tunable} boundary phase-twist. The latter may
induce ``persistent currents'', visible by studing the atoms' momentum
distribution. We show how important phenomena in 1d-physics can be studied by
physical realization of systems of trapped atoms in ring-shaped optical
lattices. A mixture of bosonic and/or fermionic atoms can be loaded into the
lattice, realizing a generic quantum system of many interacting particles.Comment: 10 pages, 5 figures. To be published in PR
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
Exact relationship between the entanglement entropies of XY and quantum Ising chains
We consider two prototypical quantum models, the spin-1/2 XY chain and the
quantum Ising chain and study their entanglement entropy, S(l,L), of blocks of
l spins in homogeneous or inhomogeneous systems of length L. By using two
different approaches, free-fermion techniques and perturbational expansion, an
exact relationship between the entropies is revealed. Using this relation we
translate known results between the two models and obtain, among others, the
additive constant of the entropy of the critical homogeneous quantum Ising
chain and the effective central charge of the random XY chain.Comment: 6 page
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