Detection of Symmetry Enriched Topological Phases

Topologically ordered systems in the presence of symmetries can exhibit new structures which are referred to as symmetry enriched topological (SET) phases. We introduce simple methods to detect the SET order directly from a complete set of topologically degenerate ground state wave functions. In particular, we first show how to directly determine the characteristic symmetry fractionalization of the quasiparticles from the reduced density matrix of the minimally entangled states. Second, we show how a simple generalization of a non-local order parameter can be measured to detect SETs. The usefulness of the proposed approached is demonstrated by examining two concrete model states which exhibit SET: (i) a spin-1 model on the honeycomb lattice and (ii) the resonating valence bond state on a kagome lattice. We conclude that the spin-1 model and the RVB state are in the same SET phases

Deterministic Dense Coding and Faithful Teleportation with Multipartite Graph States

We proposed novel schemes to perform the deterministic dense coding and faithful teleportation with multipartite graph states. We also find the sufficient and necessary condition of a viable graph state for the proposed scheme. That is, for the associated graph, the reduced adjacency matrix of the Tanner-type subgraph between senders and receivers should be invertible.Comment: 10 pages, 1 figure;v2. discussions improve

Detecting and identifying 2D symmetry-protected topological, symmetry-breaking and intrinsic topological phases with modular matrices via tensor-network methods

Symmetry-protected topological (SPT) phases exhibit nontrivial order if symmetry is respected but are adiabatically connected to the trivial product phase if symmetry is not respected. However, unlike the symmetry-breaking phase, there is no local order parameter for SPT phases. Here we employ a tensor-network method to compute the topological invariants characterized by the simulated modular $S$ and $T$ matrices to study transitions in a few families of two-dimensional (2D) wavefunctions which are $\mathbb{Z}_N$ ($N=2\, \&3$) symmetric. We find that in addition to the topologically ordered phases, the modular matrices can be used to identify nontrivial SPT phases and detect transitions between different SPT phases as well as between symmetric and symmetry-breaking phases. Therefore, modular matrices can be used to characterize various types of gapped phases in a unifying way

Experimental and Numerical Investigations on Dynamic Characteristics for Piezoceramic Bimorphs

Piezoceramic bimorph structures have been widely used in recent years as they combine the advantages of different materials. Two thin layers of piezoelectric ceramic are bonded together with the central layer of metal and are electrically connected in parallel and series. The structure produces large strokes with relatively low voltage because of its special bimorph concept. It is necessary to investigate the resonant characteristics of the bimorphs theoretically and experimentally to facilitate the industrial applications. In this study, three experimental techniques are employed to access the resonant characteristics of the bimorphs. These experimental methods are the electronic speckle pattern interferometry (ESPI), laser Doppler vibrometer (LDV), and impedance analysis. Finally, numerical computations based on the finite element method are presented and compared with the experimental measurements. Good agreements of resonant frequencies and mode shapes are obtained from the experimental and numerical results

Multipartite Entanglement Measures and Quantum Criticality from Matrix and Tensor Product States

We compute the multipartite entanglement measures such as the global entanglement of various one- and two-dimensional quantum systems to probe the quantum criticality based on the matrix and tensor product states (MPSs/TPSs). We use infinite time-evolving block decimation (iTEBD) method to find the ground states numerically in the form of MPSs/TPSs, and then evaluate their entanglement measures by the method of tensor renormalization group (TRG). We find these entanglement measures can characterize the quantum phase transitions by their derivative discontinuity right at the critical points in all models considered here. We also comment on the scaling behaviors of the entanglement measures by the ideas of quantum state renormalization group transformations.Comment: 22 pages, 11 figure