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The commensurate and incommensurate Haldane phases for the spin-1 bilinear-biquadratic model are investigated using the infinite matrix product state algorithm. The bipartite entanglement entropy can detect a transition point between the two phases. In both phases, the entanglement spectrum shows the double degeneracy. We calculate the nonlocal order parameter of the bond-centered inversion in both phases, which rapidly approaches a saturation value -1 as the segment length increases. The nonlocal order parameter of the bond-centered inversion with a saturation value -1 and the nonzero value string order indicate that the Haldane phase is a symmetry-protected topological phase. To distinguish the commensurate and incommensurate Haldane phases, the transversal spin correlation and corresponding momentum distribution of the structure factor are analyzed. As a result, the transversal spin correlations exhibit different decay forms in both phases.

With the development of microelectronics and the miniaturization of electronic devices, the use of molecular materials to construct various components in electronic circuits has become a most likely development trend. Compared with silicon-based semiconductor components, molecular electronic device has the advantages of small size, high integration, low energy consumption and fast response. In recent years, more and more molecules have been used to design molecular devices such as molecular diodes, molecular switches, molecular field effect transistors and molecular memories. In this paper, sandwich structure devices based on graphene nanoribbon electrodes are constructed. The first-principles calculation method combining density functional theory and non-equilibrium Green’s function is adopted to design the molecular devices with functional characteristics. The effects of redox reactions on the electrical transport properties of molecular devices are systematically discussed. The main research contents of this paper are as follows. The switching characteristics of an anthraquinone molecular device based on graphene electrode are studied. The zigzag-edge nanoribbons and armchair-edge graphene nanoribbons are selected as electrodes. Considering the two isomers of anthraquinone (HQ) and anthraquinone (AQ) molecules in the redox reaction, the double electrode molecular junction is constructed. The effects of redox reaction and electrode structure on the switching characteristics of anthraquinone molecular devices are discussed. It is found that the current in the HQ configuration is significantly greater than that in the AQ configuration, regardless of the zigzag-edge graphene electrode or the armchair-edge graphene electrode. That is, under the redox reaction, the anthraquinone molecules show significant switching characteristics. The switching ratio of zigzag-edge graphene electrode is selected to reach a maximum of 3125, and that of armchair-edge graphene electrode is selected to maximum of 1538. In addition, when the armchair-edge graphene is used as an electrode in the HQ configuration, the negative differential resistance is obviously between 0.7 and 0.9 V.

Quantum phase transitions are driven by quantum fluctuations due to the uncertainty principle in many-body physics. In quantum phase transitions, the ground-state changes dramatically. The quantum entanglement, specific heat, magnetization and other physical quantities diverge according to certain functions, and show specific scaling behaviors. In addition, there is a topological quantum phase transition beyond the conventional Landau-Ginzburg-Wilson paradigm, which is relevant to emergent phenomena in strongly correlated electron systems, with topological nonlocal order parameters as a salient feature. Thus, topological order is a new paradigm in the study of topological quantum phase transitions.To investigate competition mechanism of the different quantum spin interactions, in this paper, the one-dimensional spin-1 bond-alternating Heisenberg model with Dzyaloshinskii-Moriya (DM) interaction is considered. The DM interaction drives the quantum fluctuations resulting in a phase transition. By using the one-dimensional infinite matrix product state algorithm in tensor network representation, the quantum entanglement entropy and order parameters are calculated from the ground-state function. The numerical result shows that with the change of bond alternating strength, there is a quantum phase transition from the topological ordered Haldane phase to the local ordered dimer phase. Based on the von Neumann entropy and order parameter, the phase diagram of this model is obtained. There is a critical line that separates the Haldane and the dimer phase. The DM interaction inhibits the dimerization of the quantum spin system and finally breaks the fully dimerization. Due to the fact that the structurally symmetry of system is broken, the local dimer order exists in the whole parameter range when the bond-alternative strength parameter changes. The first derivative of the local dimer order behaves as a peak corresponding to the critical point. Furthermore, from the numerical scaling of the first derivative of dimer order and the non-local string order near the phase transition point, the characteristic critical exponents α and β are obtained, respectively. It shows that the characteristic critical exponent α decreases, and β increases gradually with the interaction strength of DM increasing. The resulting state i.e. the anti-symmetric anisotropic DM interaction produced by spin-orbit coupling, affects the critical properties of the system in the phase transition. This reveals that the competition mechanism of the quantum spin interaction, also provides some guidance for the future study of the critical behavior in topological quantum phase transition with the DM interaction.

The scaling behavior of physical observable in the phase transition point for one-dimensional quantum two-spin and three-spin model is investigated by employing the infinite matrix product state representation with the infinite time evolving block decimation method. The analytical results, which are checked numerically finding excellent agreement for the model with central charge c = 4/5 , demonstrate that the scaling behavior with finite truncation dimension $ \chi$ in local Hilbert space can be employed to characterize the one-dimensional quantum spin model. Meanwhile, the infinite time evolving block decimation algorithm by the infinite matrix product state representation can be a quite accurate method to obtain the critical properties at continuous phase transition point.

Quantum correlation and interference effects are investigated in mesoscopic interferometers connected to a normal metal and a superconductor. For quasiparticle excitation energies smaller than superconducting gap, a Fano-Andreev antiresonance for zero excitation energy is shown to be split into two zero-transmissions located at energies lower and higher than the Fano-Andreev antiresonance energy. For an excitation energy bigger than the gap, the higher energy antiresonance disappears for electron-like quasiparticle transport. In the presence of a superconductor interface potential Z, we find that the transport and the circulating currents normalized by their amplitudes for a clean interface have the same I(Z)-Z curve. We discuss a transition among the three types of normalized currents, which shows a characteristic transition diagram in association with the excitation energy. Also, as a demonstration of the existence of Andreev holes, we show that only the Andreev hole current can circulate along the interferometer loop.

Coherent quantum tunneling effects on quantum interference are investigated in electron transport through a mesoscopic interferometer. An evanescent wave tunneling through a potential barrier in one arm can interfere with a propagating wave passing through the other arm of the interferometer. It is shown that, even for the same arm lengths, such a quantum interference can induce a circulating current, where Fano antiresonances do not occur in electron transmission. It is found that there exists a critical value of asymmetric arm lengths that gives rise to a Fano antiresonance in electron transmission for quantum interference between evanescent and propagating waves. We discuss the effects of Fano antiresonances originating from asymmetric arm lengths on circulating currents.

With the experimental advances in microscale fabrication technology, the designing of functional devices by using single molecules has become one of the most promising methods for the next generation of electronic devices. Molecular rectifier, as a basic component almost for any electronic device, has become a research hotspot in molecular electronics. Recently, one-dimensional graphene nanoribbons (GNRs) which cut off from the novel two-dimensional material-graphene were used as the electrodes for several molecular devices due to their unique electronic structures and transport characteristics. The GNRs have less serious contact problems than metallic electrode materials like gold. In this paper, we investigate the rectifying performances of oligo phenylene ethynylene molecular devices based on graphene electrodes by using the density-functional theory and the non-equilibrium Green's function method. The effect of functional group on the rectifying performances of molecular device is discussed. The results show that the functional group plays a significant role in determining the rectifying performances of oligo phenylene ethynylene molecular device. The rectifying ratio can be effectively tuned by the functional group: adding the donor group (NH2) can lead to the positive rectifying phenomenon, adding the acceptor group (NO2) can trigger the negative rectifying phenomenon, and simultaneously adding NH2 and NO2 groups can bring about an alternate phenomenon between positive and reverse rectifying . The physical mechanism of the rectifying behavior is explained based on the transmission spectra and molecular projected self-consistent Hamiltonian. The transmission spectra of four models (M1-M4) bias voltages in range from-1.0 V to 1.0 V are given. The main transmission peak of M1 for positive bias is similar to that for negative bias, resulting in a weak rectification ratio. However, for M2 and M3, the main transmission peaks for positive and negative bias are significantly different from each other, which shows obviously a rectifying behavior. For M4, the main transmission peak is higher for the bias of (0.44-0.83 V) and also for the bias (0.95-1.00 V), showing an alternate phenomenon between positive and reverse rectifying. The maximum rectification ratio reaches 2.71 by adding an acceptor group (NO2), which suggests that this system has attractive potential applications in future molecular circuit.

Quantum entanglement for a one-dimensional quantum antiferromagnetic-ferromagnetic spin-1/2 alternating Heisenberg chain is investigated by employing the infinite matrix product state representation. The entanglement entropies for the model are shown and the peaks of the entropies tell us the quantum phase transitions happen when the control parameter crosses its critical value. Besides, spontaneous magnetization is given and the critical exponent is extracted from the data. Finally, a finite-entanglement scaling of the von Neumann entropy and finite-entanglement scaling exponent are given with different truncation dimension, from which the type of the transition and its conformal anomaly parameter c are obtained at the critical point.

The characterization of the quantum phase transition in a lowdimensional system has attracted a considerable amount of attention in quantum manybody systems. As one of the fundamental models in quantum magnetism, spin-1 models have richer phase diagrams and show more complex physical phenomena. In the spin-1 antiferromagnetic XXZ model, the Haldane phase and the Nel phase are the gapped topologic phases which cannot be characterized by the local order parameters. To characterize the nature in such phases, one has to calculate the non-local long range order parameters. Normally, the non-local order parameter in the topological phase is obtained from the extrapolation of finite-sized system in numerical study. However, it is difficult to extract the critical exponents with such an extrapolated non-local order parameter due to the numerical accuracy. In a recently developed tensor network representation, i.e., the infinite matrix product state (iMPS) algorithm, it was shown that the non-local order can be directly calculated from a very large lattice distance in an infinite-sized system rather than an extrapolated order parameter in a finite-sized system. Therefore, it is worthwhile using this convenient technique to study the non-local orders in the topological phases and characterize the quantum criticalities in the topological quantum phase transitions. In this paper, by utilizing the infinite matrix product state algorithm based on the tensor network representation and infinite time evolving block decimation method, the quantum entanglement, fidelity, and critical exponents of the topological phase transition are investigated in the one-dimensional infinite spin-1 bond-alternating XXZ Heisenberg model. It is found that there is always a local dimerization order existing in the whole parameter range when the bond-alternative strength parameter changes from 0 to 1. Also, due to the effect of the bond-alternating, there appears a quantum phase transition from the long-rang ordering topological Nel phase to the local ordering dimerization phase. The von Neumann entropy, fidelity per lattice site, and order parameters all give the same phase transition point at c = 0.638. To identify the type of quantum phase transition, the central charge c 0.5 is extracted from the ground state von Neumann entropy and the finite correlation length, which indicates that the phase transition belongs to the two-dimensional Ising universality class. Furthermore, it is found that the Nel order and the susceptibility of Nel order have power-law relations to |-c|. From the numerical fitting of the Nel order and its susceptibility, we obtain the characteristic critical exponents ' = 0.236 and ' = 0.838. It indicates that such critical exponents from our method characterize the nature of the quantum phase transition. Our critical exponents from the iMPS method can provide guidance for studying the properties of the phase transition in quantum spin systems.

String correlations are investigated in an infinite-size XXZ spin-1 chain. By using the infinite matrix product state representation, we calculate a long-range string order. In the XY phase, the string correlations decay within a relatively very large lattice distance, which makes a finite-size study difficult to verify the non-existence of the string order. Thus, in the Haldane phase, the non-vanishing string correlations in the limit of a very large distance allow to characterize the phase boundaries to the XY phase and the Neel phase, which implies that the transverse long-range string order is the order parameter for the Haldane phase. In addition, the singular behaviors of the von Neumann entropy and the fidelity per lattice site are shown to capture clearly the phase transition points that are consistent with the results from the string order. The estimated critical points including a BKT transition from the XY phase to the Haldane phase agree well with the previous results: $\Delta_{c2} = 0$ for the XY-Haldane phase transition and $\Delta_{c3} = 1.185$ for the Haldane-N'eel phase transition from the density renormalization group. From a finite-entanglement scaling of the von Neumann entropy with respect to the truncation dimension, the central charges are found to be $c \simeq 1.0$ at $\Delta_{c2} = 0$ and $c \simeq 0.5$ at $\Delta_{c3} = 1.185$, respectively, which shows that the XY-Haldane phase transition at $\Delta_{c2} = 0$ belongs to the Heisenberg universality class, while the Haldane-Neel phase transition at $\Delta_{c2} = 1.185$ belongs to the two-dimensional classical Ising universality class. It is also shown that, the long-range order parameters and the von Neumann entropy, as well as the fidelity per site approach, can be applied to characterize quantum phase transitions as a universal phase transition indicator for one-dimensional lattice many-body systems., Comment: 12 pages, 12 figures

An investigation of the microstructure and the microprocess of fracture of an eutectoid pearlitic steel has been carried out by means of electron-diffraction-contrast (EDC) and other analytical techniques. The nature of the dislocations in pro-eutectoid ferrite and ferrite in pearlite was determined. The character of interface conjunction between ferrite and cementite was discussed. The fracture process of pearlitic steel has been analysed crystallographically.