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

Directed percolation near a wall

Series expansion methods are used to study directed bond percolation clusters on the square lattice whose lateral growth is restricted by a wall parallel to the growth direction. The percolation threshold $p_c$ is found to be the same as that for the bulk. However the values of the critical exponents for the percolation probability and mean cluster size are quite different from those for the bulk and are estimated by $\beta_1 = 0.7338 \pm 0.0001$ and $\gamma_1 = 1.8207 \pm 0.0004$ respectively. On the other hand the exponent $\Delta_1=\beta_1 +\gamma_1$ characterising the scale of the cluster size distribution is found to be unchanged by the presence of the wall. The parallel connectedness length, which is the scale for the cluster length distribution, has an exponent which we estimate to be $\nu_{1\parallel} = 1.7337 \pm 0.0004$ and is also unchanged. The exponent $\tau_1$ of the mean cluster length is related to $\beta_1$ and $\nu_{1\parallel}$ by the scaling relation $\nu_{1\parallel} = \beta_1 + \tau_1$ and using the above estimates yields $\tau_1 = 1$ to within the accuracy of our results. We conjecture that this value of $\tau_1$ is exact and further support for the conjecture is provided by the direct series expansion estimate $\tau_1= 1.0002 \pm 0.0003$.Comment: 12pages LaTeX, ioplppt.sty, to appear in J. Phys.

Exploring the Referral and Usage of Science Fiction in HCI Literature

Research on science fiction (sci-fi) in scientific publications has indicated the usage of sci-fi stories, movies or shows to inspire novel Human-Computer Interaction (HCI) research. Yet no studies have analysed sci-fi in a top-ranked computer science conference at present. For that reason, we examine the CHI main track for the presence and nature of sci-fi referrals in relationship to HCI research. We search for six sci-fi terms in a dataset of 5812 CHI main proceedings and code the context of 175 sci-fi referrals in 83 papers indexed in the CHI main track. In our results, we categorize these papers into five contemporary HCI research themes wherein sci-fi and HCI interconnect: 1) Theoretical Design Research; 2) New Interactions; 3) Human-Body Modification or Extension; 4) Human-Robot Interaction and Artificial Intelligence; and 5) Visions of Computing and HCI. In conclusion, we discuss results and implications located in the promising arena of sci-fi and HCI research.Comment: v1: 20 pages, 4 figures, 3 tables, HCI International 2018 accepted submission v2: 20 pages, 4 figures, 3 tables, added link/doi for Springer proceedin

A logarithmic generalization of tensor product theory for modules for a vertex operator algebra

We describe a logarithmic tensor product theory for certain module categories for a ``conformal vertex algebra.'' In this theory, which is a natural, although intricate, generalization of earlier work of Huang and Lepowsky, we do not require the module categories to be semisimple, and we accommodate modules with generalized weight spaces. The corresponding intertwining operators contain logarithms of the variables.Comment: 39 pages. Misprints corrected. Final versio

Quantitative rescattering theory for laser-induced high-energy plateau photoelectron spectra

A comprehensive quantitative rescattering (QRS) theory for describing the production of high-energy photoelectrons generated by intense laser pulses is presented. According to the QRS, the momentum distributions of these electrons can be expressed as the product of a returning electron wave packet with the elastic differential cross sections (DCS) between free electrons with the target ion. We show that the returning electron wave packets are determined mostly by the lasers only, and can be obtained from the strong field approximation. The validity of the QRS model is carefully examined by checking against accurate results from the solution of the time-dependent Schr\"odinger equation for atomic targets within the single active electron approximation. We further show that experimental photoelectron spectra for a wide range of laser intensity and wavelength can be explained by the QRS theory, and that the DCS between electrons and target ions can be extracted from experimental photoelectron spectra. By generalizing the QRS theory to molecular targets, we discuss how few-cycle infrared lasers offer a promising tool for dynamic chemical imaging with temporal resolution of a few femtoseconds.Comment: 19 pages, 19 figure