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Permutation group approach to the one-dimensional XXX Heisenberg open spin-1/2 chain with nearest neighbor interaction is proposed, which is formulated not only for half-filling excitations, but also for general case. Regularity of energy matrices and the corresponding wavefunctions are made up by using an induction method, which makes it possible to study the eigenvalue problem systematically. A Mathematica package for generating the energy matrices is implemented according to this procedure.

The thermal quantum correlations of a three-qubit spin chain of XY type under an in-homogeneous magnetic field have been investigated, where by considering magnetic fields with different magnitudes ${ℬ}-b$, ${ℬ}$ and ${ℬ}+b$ for each spin, the quantum correlations between the adjacent and the non-adjacent qubits (spins) have been studied. For this purpose, the concurrence as an entanglement quantifier and the trace distance discord as a discord-like quantifier have been computed for the corresponding bipartite subsystems with the reduced density matrices ${\rho }^{(12)}$, ${\rho }^{(23)}$ and ${\rho }^{(13)}$. The differences between the concurrence and the trace distance discord, are explained in detail. Their dependence on the parameters of the uniform magnetic field ${ℬ}$, the temperature $T$, and the in-homogeneity parameter $b$ is discussed so that the thermal correlation decreases by increasing the mentioned parameters. Also, the results show that by changing and controlling the parameters ${ℬ}$, $T$ and $b$, especially the in-homogeneous magnetic field $b$, it is possible that the correlation value between non-adjacent spins, i.e. $c({\rho }^{(13)})$ can be reached to a greater value than the thermal correlations between adjacent spins, i.e. $c({\rho }^{(12)})$ and $c({\rho }^{(23)})$. Moreover, it is shown that the trace distance $D_T^{(13)}(\rho )$ between the non-adjacent spins has always a lower value than those of the adjacent spins $D_T^{(12)}(\rho )$ and $D_T^{(23)}(\rho )$. Finally, the results show that in-homogeneous magnetic field b can be effective for improving thermal quantum correlation.

We find a new family of classical oscillating strings with large winding numbers, which are constructed by interchanging τ and σ of helical strings' solutions. We also give a finite-gap interpretation of interchanging τ and σ. Gauge dual operators are discussed at the end.

In this paper, we propose and analyze an efficient high-dimensional quantum state transfer (QST) scheme through an XXZ-Heisenberg spin chain in an inhomogeneous magnetic field. By the use of a combination of coherent quantum coupling and free spin wave approximation, pure unitary evolution results in a perfect high-dimensional swap operation between two remote quantum registers mediated by a uniform quantum data bus and the feasibility is confirmed by numerical simulations. Also, we observe that either the strong z-directional coupling or high quantum spin number can partly suppress the thermal excitations and protect quantum information from the thermal noises when the quantum data bus is in the thermal equilibrium state.

The ground state of a spin-1/2 ring in the Heisenberg XY model is investigated. The spatial correlation and concurrence between an arbitrary nearest-neighbor pair of spins are calculated with different coupling strength, anisotropic parameter and magnitude of the transverse field. Abrupt changes of the correlation and concurrence due to the competition between coupling and alignment are observed. The transition is found to be the direct result of the level crossing of a finite size spin system.

In this paper, we investigate the nonequilibrium geometric phase (GP) of a spin chain system whose two end spins are respectively coupled to thermal reservoirs at different temperatures. In the spin chain, there exists the XX-type spin interaction and an external field is applied to each spin. An analytical expression for the GP is found in the weak coupling limit. The influences of various parameters on the deviation of GP from the unitary one are investigated. It is found that the GP is more stable against the decoherence when the external field is homogenously applied. In addition, the present result may provide a useful approach to the maintenance of GP in the nonequilibrium system.

The quantum teleportation via thermally entangled states of three-qubit Heisenberg spin chains with Dzyaloshinsky–Moriya (DM) interactions under a homogeneous magnetic field has been investigated. It is found that average fidelity and critical temperature depend on not only temperature, magnetic field, but also coupling coefficients, and DM interactions. What is more, we also find that average fidelity has little to do with entanglement.

In this paper, we numerically study the non-Abelian statistics of the zero-energy Majorana fermions at the end of Majorana chain and show its application to quantum computing by mapping it to a spin model with special symmetry. In particular, by using transverse-field Ising model with Z2 symmetry, we verify the nontrivial non-Abelian statistics of Majorana fermions. Numerical evidence and comparison in both Majorana representation and spin representation are presented. The degenerate ground states of a symmetry protected spin chain therefore provide a promising platform for topological quantum computation.

The long-range interacting spin-1 chain placed in a staggered magnetic field is studied by means of microcanonical approach. Firstly, we study the microcanonical entropy of the system in the thermodynamic limit and find the system is non-ergodic and can exhibit either first-order phase transition or second-order phase transition by shifting the external magnetic field strength. Secondly, we construct the global phase diagram of the system and find a phase transition area in the phase diagram corresponding to the temperature jump of the first-order phase transition.

A long-range interacting Fermi chain placed in the uniform and the staggered magnetic field is studied via the micro-canonical approach. The relation between the entropy and the energy of the system is obtained by counting the number of microscopic states. We find that this system is non-ergodic and can exhibit first-order phase transition, second-order phase transition, or both. The microcanonical ensemble predicts negative specific heat regions and temperature jumps. Moreover, the global phase diagram of the system is constructed.

A long-range interacting spin chain can exhibit temperature jump at the transition energy under the microcanonical description. After two identical long-range interacting subsystems of the same size at the same temperatures are weakly coupled, they exchange energy and the total microcanonical entropy of the full system increases irreversibly, leading to a violation of the Zeroth Law of Thermodynamics. In addition, microcanonical Monte Carlo simulations are performed to verify our conclusion.

We study the ground-state entanglement properties of an XX spin 1/2 chain in transverse field, in its quasi-long-ranged ordered phase, with a magnetic impurity, represented in terms of an additional transverse magnetic field located at one precise site. For such a system, we show that a control of the ground state entanglement can be achieved by acting on the impurity field. To demonstrate this possibility, we evaluate exactly the nearest neighbor and next-nearest neighbor concurrence in the presence of the impurity. It turns out that either an enhancement or a quenching of entanglement between selected spin pairs can be obtained by acting on the intensity of the impurity. For specific values of the magnetic field a spatial modulation of concurrence along the chain is also obtained.

We investigate the transfer of bipartite (measured by cocurrence) and multipartite (measured by global discord) quantum correlations though spin chains under phase decoherence. The influence of phase decoherence and anisotropy parameter upon quantum correlations transfer is investigated. On the one hand, in the case of no phase decoherence, there is no steady state quantum correlations between spins. On the other hand, if the phase decoherence is larger than zero, the bipartite quantum correlations can be transferred through a Heisenberg XXX chain for a long time and there is steady state bipartite entanglement. For a Heisenberg XX chain, bipartite entanglement between two spins is destroyed completely after a long time. Multipartite quantum correlations of all spins are more robust than bipartite quantum correlations. Thus, one can store multipartite quantum correlations in spin chains for a long time under phase decoherence.

The relationship between entanglement and anisotropy is studied in small spin chains with periodic boundary conditions. The Hamiltonian of the spin chains is given by a slight modification of the dipolar Hamiltonian. The effect of the anisotropy is analyzed using the concurrence shared by spin pairs, but the study is not restricted to nearest-neighbor (NN) entanglement. It is shown that, under rather general conditions, the inclusion of anisotropic terms diminishes the entanglement shared between the spins of the chain irrespective of its range or its magnetic character.

We combine the long-distance quantum state transfer and simple operations with the elements of the transferred (nor perfectly) density matrix. These operations are turning some matrix elements to zero, rearranging the matrix elements and preparing their linear combinations with required coefficients. The basic tool performing these operations is the unitary transformation on the extended receiver. A system of linear algebraic equations can be solved in this way as well. Such operations are numerically simulated on the basis of 42-node spin-1/2 chain with the two-qubit sender and receiver.

Using Monte Carlo simulation and mean field approximation, we studied the magnetic properties of spin-3/2 chain with hexagonal spin-1/2 shell and negative core-shell exchange coupling. The obtained results show that the spins 3/2 in the core have an important influence on the magnetic behavior of the system such as the appearance of compensation temperatures as well as first- and second-order phase transitions. Moreover, we investigated the effects of exchange interactions and anisotropy on the phase diagrams of the system.