Quantum phase transition and von Neumann entropy of quasiperiodic Hubbard chains

The half-filled Hubbard chains with the Fibonacci and Harper modulating site potentials are studied in a selfconsistent mean-field approximation. A new order parameter is introduced to describe a charge density order. We also calculate the von Neumann entropy of the ground state. The results show that the von Neumann entropy can identify a CDW/SDW （charge density wave/spin density wave） transition for quasiperiodic models.

Perturbation theory of von Neumann entropy

In quantum information theory, yon Neumann entropy plays an important role; it is related to quantum channel capacities. Only for a few states can one obtain their entropies. In a continuous variable system, numeric evaluation of entropy is not easy due to infinite dimensions. We develop the perturbation theory for systematically calculating von Neumann entropy of a non-degenerate system as well as a degenerate system.

Analytical and numerical investigations of displaced thermal state evolutions in a laser process

We investigate how displaced thermal states （DTSs） evolve in a laser channel. Remarkably, the initial DTS, an example of a mixed state, still remains mixed and thermal. At long times, they finally decay to a highly classical thermal field only related to the laser parameters κ and g. The normal ordering product of density operator of the DTS in the laser channel leads to obtaining the analytical time-evolution expressions of the photon number, Wigner function, and von Neumann entropy. Also, some interesting results are presented via numerically investigating these explicit time-dependent expressions.

Entanglement property in matrix product spin systems

We study the entanglement property in matrix product spin-ring systems systemically by von Neumann entropy. We find that： （i） the Hilbert space dimension of one spin determines the upper limit of the maximal value of the entanglement entropy of one spin, while for multiparticle entanglement entropy, the upper limit of the maximal value depends on the dimension of the representation matrices. Based on the theory, we can realize the maximum of the entanglement entropy of any spin block by choosing the appropriate control parameter values. （ii） When the entanglement entropy of one spin takes its maximal value, the entanglement entropy of an asymptotically large spin block, i.e. the renormalization group fixed point, is not likely to take its maximal value, and so only the entanglement entropy Sn of a spin block that varies with size n can fully characterize the spin-ring entanglement feature. Finally, we give the entanglement dynamics, i.e. the Hamiltonian of the matrix product system.

Total versus quantum correlations in a two-mode Gaussian state

In Li and Luo(2007 Phys.Rev.A 76032327),the inequality(1/2)T≥Q was identified as a fundamental postulate for a consistent theory of quantum versus classical correlations for arbitrary measures of total T and quantum Q correlations in bipartite quantum states.Besides,Hayden et al(2006 Commun.Math.Phys.26595)have conjectured that,in some conditions within systems endowed with infinite-dimensional Hilbert spaces,quantum correlations may dominate not only half of total correlations but total correlations itself.Here,in a two-mode Gaussian state,quantifying T and Q respectively by the quantum mutual information I~G and the entanglement of formation(EoF)ε_(F)^(G),we verify thatε_(F)^(G),is always less than(1/2)I_(R)^(G( when I~G andε_(F)^(G) are defined via the Rényi-2 entropy.While via the von Neumann entropy,ε_(F,V)^(G),may even dominate I_(V)^(G) itself,which partly consolidates the Hayden conjecture,and partly,provides strong evidence hinting that the origin of this counterintuitive behavior should intrinsically be related to the von Neumann entropy by which the EoFε_(F,V)^(G),is defined,rather than related to the conceptual definition of the EoFε_(F).The obtained results show that—in the special case of mixed two-mode Gaussian states—quantum entanglement can be faithfully quantified by the Gaussian Rényi-2 EoFε_(F,R)^(G),.