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We carry out an extensive study, within the infinite matrix product state algorithm, one-dimensional spin-1 Blume–Capel model on the spin-chain and subject to a changeable external magnetic field. The phase transition points are obtained by investigating the behavior of physical observable and as well as exacting the critical exponent from the scaling relationship. The final results are achieved for the physical observable-quantum entanglement entropy, local order parameter and its scaling: the scaling relationship between quantum entanglement entropy and truncation dimension, the scaling of Schmidt decomposition coefficient λ m a x and truncation dimension, the critical exponent of local order parameter near the phase transition point is extracted with the scaling behavior for the model with exchange coupling γ = 0 . 6 . These techniques are an easy way to exact the critical exponent for quantum phase transitions.

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.

We investigated the quantum phase transition occurred in one-dimensional quantum Heisenberg XYZ model with Dzyaloshinskii–Moriya interaction via the infinite matrix product state representation with the infinite time evolving block decimation method. Entanglement entropy and local order parameter in and near the transition point are given. Scaling relation plays crucial roles on identifying a quantum system with a physically different phase. The scaling relation of the entanglement entropy, local order parameter and finite correlation length with the truncation dimension are also obtained. All the interesting results give a theoretical justification for the high accuracy of infinite time evolved block decimation algorithm which works in the thermodynamical limit.

Based on the tensor network representations, we have developed an efficient scheme to calculate the global geometric entanglement as a multipartite entanglement measure for the three-leg spin tubes. From the geometric entanglement, the phase diagram of a spin-3 / 2 isosceles triangle spin tube has been investigated varying the base interaction α. Two Berezinsky-Kosterlitz-Thouless phase transitions are estimated to be α c1 ≃ 0.68 and α c2 ≃ 3.85, respectively. Then, even though the spin tube is in gapless spin liquid phases for α < α c1 and α > α c2, the geometrical structure difference between the groundstate wavefunctions for the two regions is found to reflect the global geometric entanglement that contains bipartite and multipartite contributions. Further, the phase transition points from the von Neumann entropies and fidelity are consistent with that from the geometric entanglement. As a result, the global geometric entanglement can be used to explore a geometrical nature of quantum phases as well as an indicator for quantum phase transitions in many-body lattice systems.

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.

Dimerized phase and quantum entanglement are investigated in the one-dimensional spin-1 bilinear biquadratic model. Employing the infinite matrix product state representation, groundstate wavefunctions are numerically obtained by using the infinite time evolving block decimation method in the infinite lattice system. From a bipartite entanglement measure of the groundstates, i.e., von Neumann entropy, the phase transition points can be clearly extracted. Moreover, the even-bond and odd-bond von Neumann entropies show two different values in the spontaneous dimerized phase. It implies that the quantum entanglement can distinguish the two degenerate groundstates. Then, we define a dimer entropy in the spontaneous dimerized phase. Comparing to the dimer order parameter, the dimer entropy can play a role of a local order parameter to characterize the spontaneous dimerized phase.

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.

UnISIS (University of Illinois Seeing Improvement System) is a versatile adaptive optics system mounted on a large optics bench at the coude focus of the Mount Wilson 2.5-m telescope. It was designed to have both laser guide star (LGS) and natural guide star (NGS) adaptive optics capabilities. The LGS side of the system relies on a pulsed UV laser with raw power of 30 W capable of creating an artificial laser star via Rayleigh scattering 18 km above the telescope. The LGS system can work at temporal response rates as high as 333 Hz-limited by the UV laser pulse rate-and the NGS system can work at rates up to 1.4 kHz. Each side of the system has its own highspeed wavefront sensor that runs separately, but in the LGS mode the NGS wavefront sensor is converted into a natural star tip-tilt sensor. The deformable mirror is conjugate to the telescope's primary mirror and has one of the most densely packed sets of actuators of any adaptive optics system currently in operation. This paper provides details of the UnISIS design and describes key updates we have made to the system. We show NGS AO-corrected images from the sky from the 900 nm z-band through the 2.12 mu m K(s) band. The highest NGS Strehl achieved to date is 0.67 at K(s) band.

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.

Ground-state entanglement entropies were investigated for the one-dimension quantum two- and three-spin interaction models, the four-state Potts model, and the XXZ model with uniaxial single-ion-type anisotropy, which were obtained on an infinite-size lattice in one spatial dimension. Thus we show that the entanglement, a key concept of quantum information science, is quantified by the ground-state entanglement entropy. The relationships between ground-state entanglement entropy and quantum phase transition was analyzed. These results were obtained using the infinite matrix product state algorithm which works in the thermodynamical limit.

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.

We have developed an efficient tensor network algorithm for spin ladders, which generates ground-state wave functions for infinite-size quantum spin ladders. The algorithm is able to efficiently compute the ground-state fidelity per lattice site, a universal phase transition marker, thus offering a powerful tool to unveil quantum many-body physics underlying spin ladders. To illustrate our scheme, we consider the two-leg and three-leg Heisenberg spin ladders with staggering dimerization, the two-leg Heisenberg spin ladder with cyclic four-spin exchange, and the ferromagnetic frustrated two-leg ladder. The ground-state phase diagrams thus yielded are reliable, compared with the previous studies based on the the exact diagonalization and the density matrix renormalization group. Our results indicate that the ground-state fidelity per lattice site successfully captures quantum criticalities in spin ladders.

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

The UnISIS adaptive optics system is now completed and ready for science observations. We describe the experience we have gained in building and using the system, and we give a preview of one new science goal: the use of Gaussian aperture pupil masks for high-contrast imaging of companion objects near bright stars. A key aspect of the UnISIS design is the simultaneous use of two wavefront sensors, one for natural stars and the other for the laser guide star. We demonstrate the performance of this calibration system with results from on-the-bench tests. We describe several practical aspects of observing at Mt. Wilson including our ability to predict the nights of best seeing with weather data available on-line. We also show how the laser guide star return signal is enhanced by observing at large zenith angles and compare this to Rayleigh scattering models.