Topological phase in 1D1D topological Kondo insulator: Z2Z_{2} topological insulator, Haldane-like phase and Kondo breakdown

We have simulated a half-filled $1D$ $p$-wave periodic Anderson model with numerically exact projector quantum Monte Carlo technique, and the system is indeed located in the Haldane-like state as detected in previous works on the $p$-wave Kondo lattice model, though the soluble non-interacting limit corresponds to the conventional $Z_{2}$ topological insulator. The site-resolved magnetization in an open boundary system and strange correlator for the periodic boundary have been used to identify the mentioned topological states. Interestingly, the edge magnetization in the Haldane-like state is not saturated to unit magnetic moment due to the intrinsic charge fluctuation in our periodic Anderson-like model, which is beyond the description of the Kondo lattice-like model in existing literature. The finding here underlies the correlation driven topological state in this prototypical interacting topological state of matter and naive use of non-interacting picture should be taken care. Moreover, no trace of the surface Kondo breakdown at zero temperature is observed and it is suspected that frustration-like interaction may be crucial in inducing such radical destruction of Kondo screening. The findings here may be relevant to our understanding of interacting topological materials like topological Kondo insulator candidate SmB$_{6}$.Comment: 11 pages, 9 figures, accepted by EPJ

Superfluid density in the slave-boson theory

Despite of the success of the slave-boson theory in capturing qualitative physics of high-temperature superconductors like cuprates, it fails to reproduce the correct temperature-dependent behavior of superfluid density, let alone the independence of the linear temperature term on doping in the underdoped regimes of hole-doped cuprate, a common experimental observation in different cuprates. It remains puzzling up to now in spite of intensive theoretical efforts. For electron-doped case, even qualitative treatment is not reported at present time. Here we revisit these problems and provide an alternative superfluid density formulation by using the London relation instead of employing the paramagnetic current-current correlation function. The obtained formula, on the one hand, provides the correct temperature-dependent behavior of the superfluid density in the whole temperature regime, on the other hand, makes the doping dependence of the linear temperature term substantially weaken and a possible interpretation for its independence on doping is proposed. As an application, electron-doped cuprate is studied, whose result qualitatively agrees with existing experiments and successfully explains the origin of $d$- to anisotropic $s$-wave transition across the optimal doping. Our result remedies some failures of the slave-boson theory as employed to calculate superfluid density in cuprates and may be useful in the understanding of the related physics in other strongly correlated systems, e.g. Na$_{x}$CoO$_{2}$$\cdot$yH$_{2}$O and certain iron-based superconductors with dominating local magnetic exchange interaction.Comment: 7 pages, 4 figure

Entanglement distribution over the subsystems and its invariance

We study the entanglement dynamics of two qubits, each of which is embedded into its local amplitude-damping reservoir, and the entanglement distribution among all the bipartite subsystems including qubit-qubit, qubit-reservoir, and reservoir-reservoir. It is found that the entanglement can be stably distributed among all components, which is much different to the result obtained under the Born-Markovian approximation by C. E. L\'{o}pez {\it et al.} [Phys. Rev. Lett. \textbf{101}, 080503 (2008)], and particularly it also satisfies an identity. Our unified treatment includes the previous results as special cases. The result may give help to understand the physical nature of entanglement under decoherence.Comment: 6 pages, 5 figure