358 research outputs found
Entanglement of bosonic modes in symmetric graphs
The ground and thermal states of a quadratic hamiltonian representing the
interaction of bosonic modes or particles are always Gaussian states. We
investigate the entanglement properties of these states for the case where the
interactions are represented by harmonic forces acting along the edges of
symmetric graphs, i.e. 1, 2, and 3 dimensional rectangular lattices, mean field
clusters and platonic solids. We determine the Entanglement of Formation (EoF)
as a function of the interaction strength, calculate the maximum EoF in each
case and compare these values with the bounds found in \cite{wolf} which are
valid for any quadratic hamiltonian.Comment: 15 pages, 8 figures, 3 tables, Latex, Accepted for publication in
Physical Review
Quantum Phase Transitions and Matrix Product States in Spin Ladders
We investigate quantum phase transitions in ladders of spin 1/2 particles by
engineering suitable matrix product states for these ladders. We take into
account both discrete and continuous symmetries and provide general classes of
such models. We also study the behavior of entanglement of different
neighboring sites near the transition point and show that quantum phase
transitions in these systems are accompanied by divergences in derivatives of
entanglement.Comment: 20 pages, 6 figures, essential changes (i.e derivation of the
Hamiltonian), Revte
Equi-entangled bases in arbitrary dimensions
For the space of two identical systems of arbitrary dimensions, we introduce
a continuous family of bases with the following properties: i) the bases are
orthonormal, ii) in each basis, all the states have the same values of
entanglement, and iii) they continuously interpolate between the product basis
and the maximally entangled basis. The states thus constructed may find
applications in many areas related to quantum information science including
quantum cryptography, optimal Bell tests and investigation of enhancement of
channel capacity due to entanglement.Comment: 10 pages, 2 figures, 1 table, Accepted for publication in Phys. Rev.
Exact dimer ground states for a continuous family of quantum spin chains
Using the matrix product formalism, we define a multi-parameter family of
spin models on one dimensional chains, with nearest and next-nearest neighbor
anti-ferromagnetic interaction for which exact analytical expressions can be
found for its doubly degenerate ground states. The family of Hamiltonians which
we define, depend on 5 continuous parameters and the Majumdar-Ghosh model is a
particular point in this parameter space. Like the Majumdar-Ghosh model, the
doubly degenerate ground states of our models have a very simple structure,
they are the product of entangled states on adjacent sites. In each of these
states there is a non-zero staggered magnetization, which vanishes when we take
their translation-invariant combination as the new ground states. At the
Majumdar-Ghosh point, these entangled states become the spin-singlets
pertaining to this model. We will also calculate in closed form the two point
correlation functions, both for finite size of the chain and in the
thermodynamic limit.Comment: 11 page
Representations of the quantum matrix algebra
It is shown that the finite dimensional irreducible representaions of the
quantum matrix algebra ( the coordinate ring of ) exist only when both q and p are roots of unity. In this case th e space of
states has either the topology of a torus or a cylinder which may be thought of
as generalizations of cyclic representations.Comment: 20 page
Thermal entanglement of spins in a nonuniform magnetic field
We study the effect of inhomogeneities in the magnetic field on the thermal
entanglement of a two spin system. We show that in the ferromagnetic case a
very small inhomogeneity is capable to produce large values of thermal
entanglement. This shows that the absence of entanglement in the ferromagnetic
Heisenberg system is highly unstable against inhomogeneoity of magnetic fields
which is inevitably present in any solid state realization of qubits.Comment: 14 pages, 7 figures, latex, Accepted for publication in Physical
Review
Q-Boson Representation of the Quantum Matrix Algebra
{Although q-oscillators have been used extensively for realization of quantum
universal enveloping algebras,such realization do not exist for quantum matrix
algebras ( deformation of the algebra of functions on the group ). In this
paper we first construct an infinite dimensional representation of the quantum
matrix algebra (the coordinate ring of and then use
this representation to realize by q-bosons.}Comment: pages 18 ,report # 93-00
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