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 Mq,p(2)M_{q,p}(2)

It is shown that the finite dimensional irreducible representaions of the quantum matrix algebra $M_{ q,p}(2)$ ( the coordinate ring of $GL_{q,p}(2)$) 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 Mq(3)M_q(3)

{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 $M_q ( 3 )$(the coordinate ring of $GL_q (3))$ and then use this representation to realize $GL_q ( 3 )$ by q-bosons.}Comment: pages 18 ,report # 93-00