Case study of the uniaxial anisotropic spin-1 bilinear-biquadratic Heisenberg model on a triangular lattice

We study the spin-1 model on a triangular lattice in the presence of a uniaxial anisotropy field using a cluster mean-field (CMF) approach. The interplay among antiferromagnetic exchange, lattice geometry, and anisotropy forces Gutzwiller mean-field approaches to fail in a certain region of the phase diagram. There, the CMF method yields two supersolid phases compatible with those present in the spin-1/2 XXZ model onto which the spin-1 system maps. Between these two supersolid phases, the three-sublattice order is broken and the results of the CMF approach depend heavily on the geometry and size of the cluster. We discuss the possible presence of a spin liquid in this region.

Entanglement entropy dynamics of Heisenberg chains

By means of the time dependent density matrix renormalization group algorithm we study the zero-temperature dynamics of the Von Neumann entropy of a block of spins in a Heisenberg chain after a sudden quench in the anisotropy parameter. In the absence of any disorder the block entropy increases linearly with time and then saturates. We analyse the velocity of propagation of the entanglement as a function of the initial and final anisotropies and compare our results, wherever possible, with those obtained by means of conformal field theory. In the disordered case we find a slower ( logarithmic) evolution which may signal the onset of entanglement localization.

Structural change in multipartite entanglement sharing: A random matrix approach

We study the typical entanglement properties of a system comprising two independent qubit environments interacting via a shuttling ancilla. The initial preparation of the environments is modeled using random matrix techniques. The entanglement measure used in our study is then averaged over many histories of randomly prepared environmental states. Under a Heisenberg interaction model, the average entanglement between the ancilla and one of the environments remains constant, regardless of the preparation of the latter and the details of the interaction. We also show that, upon suitable kinematic and dynamical changes in the ancillaenvironment subsystems, the entanglement-sharing structure undergoes abrupt modifications associated with a change in the multipartite entanglement class of the overall system's state. These results are invariant with respect to the randomized initial state of the environments.

Phase diagram of spin-1 bosons on one-dimensional lattices

Spinor Bose condensates loaded in optical lattices have a rich phase diagram characterized by different magnetic order. Here we apply the density matrix renormalization group to accurately determine the phase diagram for spin-1 bosons loaded on a one-dimensional lattice. The Mott lobes present an even or odd asymmetry associated to the boson filling. We show that for odd fillings the insulating phase is always in a dimerized state. The results obtained in this work are also relevant for the determination of the ground state phase diagram of the S=1 Heisenberg model with biquadratic interaction.

Cloning transformations in spin networks without external control

In this paper we present an approach to quantum cloning with unmodulated spin networks. The cloner is realized by a proper design of the network and a choice of the coupling between the qubits. We show that in the case of phase covariant cloner the XY coupling gives the best results. In the 1 -> 2 cloning we find that the value for the fidelity of the optimal cloner is achieved, and values comparable to the optimal ones in the general N -> M case can be attained. If a suitable set of network symmetries are satisfied, the output fidelity of the clones does not depend on the specific choice of the graph. We show that spin network cloning is robust against the presence of static imperfections. Moreover, in the presence of noise, it outperforms the conventional approach. In this case the fidelity exceeds the corresponding value obtained by quantum gates even for a very small amount of noise. Furthermore, we show how to use this method to clone qutrits and qudits. By means of the Heisenberg coupling it is also possible to implement the universal cloner although in this case the fidelity is 10% off that of the optimal cloner.

Bilinear-biquadratic spin-1 chain undergoing quadratic Zeeman effect

The Heisenberg model for spin-1 bosons in one dimension presents many different quantum phases, including the famous topological Haldane phase. Here we study the robustness of such phases in front of a SU(2) symmetry-breaking field as well as the emergence of unique phases. Previous studies have analyzed the effect of such uniaxial anisotropy in some restricted relevant points of the phase diagram. Here we extend those studies and present the complete phase diagram of the spin-1 chain with uniaxial anisotropy. To this aim, we employ the density-matrix renormalization group together with analytical approaches. The complete phase diagram can be realized using ultracold spinor gases in the Mott insulator regime under a quadratic Zeeman effect.

Nonlinear excitations in ferromagnetic chains with nearest and next nearest neighbor exchange interactions

Weakly nonlinear excitations in one-dimensional isotropic Heisenberg ferromagnetic chains with nearest- and next-nearest-neighbor exchange interactions are considered. Based on the properties of modulational stability of corresponding linear spin waves, the existence regions of bright and dark magnetic solitons of the system are discussed in the whole Brillouin zone. The antidark soliton mode which is convex soliton super-imposed with a plane wave component is obtained near the zero-dispersion points of the spin wave frequency spectrum. The analytical results are checked by numerical simulations. [S0163;1829(98)01838-4].

Detection of Entanglement in Ultracold Lattice Gases

Probing non trivial magnetic ordering in quantum magnets realized with ultracold lattice gases demands detection methods with some spatial resolution built on it. Here we demonstrate that the Faraday matter-light interface provides an experimentally feasible tool to distinguish indubitably different quantum phases of a given many-body system in a non-demolishing way. We illustrate our approach by focussing on the Heisenberg chain for spin-1 bosons in the presence of a SU(2) symmetry breaking field. We explain how using the light signal obtained via homodyne detection one can reconstruct the phase diagram of the model. Further we show that the very same technique that provides a direct experimentally measurable signal of different order parameters can be extended to detect also the presence of multipartite entanglement in such systems.

A class of almost C_0(K)-C*-algebras

We consider in this paper the family of exponential Lie groups Gn,µ, whose Lie algebra is an extension of the Heisenberg Lie algebra by the reals and whose quotient group by the centre of the Heisenberg group is an ax + b-like group. The C*-algebras of the groups Gn,µ give new examples of almost C0(K)-C*-algebras.

Nonclassicality and criticality in symmetry protected magnetic phases

Quantum and global discord in a spin-1 Heisenberg chain subject to single-ion anisotropy (uniaxial field) are studied using exact diagonalisation and the density matrix renormalisation group (DMRG). We find that these measures of quantum non-classicality are able to detect the quantum phase transitions confining the symmetry protected Haldane phase and show critical scaling with universal exponents. Moreover, in the case of thermal states, we find that quantum discord can increase with increasing temperature.