Exact Results for the Bipartite Entanglement Entropy of the AKLT spin-1 chain

We study the entanglement between two domains of a spin-1 AKLT chain subject to open boundary conditions. In this case the ground-state manifold is four-fold degenerate. We summarize known results and present additional exact analytical results for the von Neumann entanglement entropy, as a function of both the size of the domains and the total system size for {\it all} four degenerate ground-states. In the large $l,L$ limit the entanglement entropy approaches $\ln(2)$ and $2\ln(2)$ for the $S^z_T=\pm 1$ and $S^z_T=0$ states, respectively. In all cases, it is found that this constant is approached exponentially fast defining a length scale $\xi=1/\ln(3)$ equal to the known bulk correlation length.Comment: 11 pages, 3 figure

How to distinguish the Haldane/Large-D state and the intermediate-D state in an S=2 quantum spin chain with the XXZ and on-site anisotropies

We numerically investigate the ground-state phase diagram of an S=2 quantum spin chain with the $XXZ$ and on-site anisotropies described by ${\mathcal H}=\sum_j (S_j^x S_{j+1}^x+S_j^y S_{j+1}^y+\Delta S_j^z S_{j+1}^z) + D \sum_j (S_j^z)^2$, where $\Delta$ denotes the XXZ anisotropy parameter of the nearest-neighbor interactions and $D$ the on-site anisotropy parameter. We restrict ourselves to the $\Delta>0$ and $D>0$ case for simplicity. Our main purpose is to obtain the definite conclusion whether there exists or not the intermediate-$D$ (ID) phase, which was proposed by Oshikawa in 1992 and has been believed to be absent since the DMRG studies in the latter half of 1990's. In the phase diagram with $\Delta>0$ and $D>0$ there appear the XY state, the Haldane state, the ID state, the large-$D$ (LD) state and the N\'eel state. In the analysis of the numerical data it is important to distinguish three gapped states; the Haldane state, the ID state and the LD state. We give a physical and intuitive explanation for our level spectroscopy method how to distinguish these three phases.Comment: Proceedings of "International Conference on Frustration in Condensed Matter (ICFCM)" (Jan. 11-14, 2011, Sendai, Japan

The Misprediction of emotions in Track Athletics.: Is experience the teacher of all things?

People commonly overestimate the intensity of their emotions toward future events. In other words, they display an impact bias. This research addresses the question whether people learn from their experiences and correct for the impact bias. We hypothesize that athletes display an impact bias and, counterintuitively, that increased experience with an event increases this impact bias. A field study in the context of competitive track athletics supported our hypotheses by showing that athletes clearly overestimated their emotions toward the outcome of a track event and that this impact bias was more pronounced for negative events than for positive events. Moreover, with increased athletic experience this impact bias became larger. This effect could not be explained by athletes’ forecasted emotions, but it could be explained by the emotions they actually felt following the race. The more experience athletes had with athletics, the less they felt negative emotions after unsuccessful goal attainment. These findings are discussed in relation to possible underlying emotion regulation processes

Observing non-ergodicity due to kinetic constraints in tilted Fermi-Hubbard chains

The thermalization of isolated quantum many-body systems is deeply related to fundamental questions of quantum information theory. While integrable or many-body localized systems display non-ergodic behavior due to extensively many conserved quantities, recent theoretical studies have identified a rich variety of more exotic phenomena in between these two extreme limits. The tilted one-dimensional Fermi-Hubbard model, which is readily accessible in experiments with ultracold atoms, emerged as an intriguing playground to study non-ergodic behavior in a clean disorder-free system. While non-ergodic behavior was established theoretically in certain limiting cases, there is no complete understanding of the complex thermalization properties of this model. In this work, we experimentally study the relaxation of an initial charge-density wave and find a remarkably long-lived initial-state memory over a wide range of parameters. Our observations are well reproduced by numerical simulations of a clean system. Using analytical calculations we further provide a detailed microscopic understanding of this behavior, which can be attributed to emergent kinetic constraints.Comment: accepted in Nature Communication

Haldane, Large-D and Intermediate-D States in an S=2 Quantum Spin Chain with On-Site and XXZ Anisotropies

Using mainly numerical methods, we investigate the ground-state phase diagram of the S=2 quantum spin chain described by $H = \sum_j (S_j^x S_{j+1}^x + S_j^y S_{j+1}^y + \Delta S_j^z S_{j+1}^z) + D \sum_j (S_j^z)^2$, where $\Delta$ denotes the $XXZ$ anisotropy parameter of the nearest-neighbor interactions and $D$ the on-site anisotropy parameter. We restrict ourselves to the case with $\Delta \ge 0$ and $D \ge 0$ for simplicity. Each of the phase boundary lines is determined by the level spectroscopy or the phenomenological renormalization analysis of numerical results of exact-diagonalization calculations. The resulting phase diagram on the $\Delta$-$D$ plane consists of four phases; the XY 1 phase, the Haldane/large-$D$ phase, the intermediate-$D$ phase and the N\'eel phase. The remarkable natures of the phase diagram are: (1) the Haldane state and the large-$D$ state belong to the same phase; (2) there exists the intermediate-$D$ phase which was predicted by Oshikawa in 1992; (3) the shape of the phase diagram on the $\Delta$-$D$ plane is different from that believed so far. We note that this is the first report of the observation of the intermediate-$D$ phase

Gas dependent hysteresis in MoS2_2 field effect transistors

We study the effect of electric stress, gas pressure and gas type on the hysteresis in the transfer characteristics of monolayer molybdenum disulfide (MoS2) field effect transistors. The presence of defects and point vacancies in the MoS2 crystal structure facilitates the adsorption of oxygen, nitrogen, hydrogen or methane, which strongly affect the transistor electrical characteristics. Although the gas adsorption does not modify the conduction type, we demonstrate a correlation between hysteresis width and adsorption energy onto the MoS2 surface. We show that hysteresis is controllable by pressure and/or gas type. Hysteresis features two well-separated current levels, especially when gases are stably adsorbed on the channel, which can be exploited in memory devices.Comment: 8 pages, 5 figure

Radon backgrounds in the DEAP-1 liquid-argon-based Dark Matter detector

The DEAP-1 \SI{7}{kg} single phase liquid argon scintillation detector was operated underground at SNOLAB in order to test the techniques and measure the backgrounds inherent to single phase detection, in support of the \mbox{DEAP-3600} Dark Matter detector. Backgrounds in DEAP are controlled through material selection, construction techniques, pulse shape discrimination and event reconstruction. This report details the analysis of background events observed in three iterations of the DEAP-1 detector, and the measures taken to reduce them. The $^{222}$Rn decay rate in the liquid argon was measured to be between 16 and \SI{26}{\micro\becquerel\per\kilogram}. We found that the background spectrum near the region of interest for Dark Matter detection in the DEAP-1 detector can be described considering events from three sources: radon daughters decaying on the surface of the active volume, the expected rate of electromagnetic events misidentified as nuclear recoils due to inefficiencies in the pulse shape discrimination, and leakage of events from outside the fiducial volume due to imperfect position reconstruction. These backgrounds statistically account for all observed events, and they will be strongly reduced in the DEAP-3600 detector due to its higher light yield and simpler geometry

Tensor network states and geometry

Tensor network states are used to approximate ground states of local Hamiltonians on a lattice in D spatial dimensions. Different types of tensor network states can be seen to generate different geometries. Matrix product states (MPS) in D=1 dimensions, as well as projected entangled pair states (PEPS) in D>1 dimensions, reproduce the D-dimensional physical geometry of the lattice model; in contrast, the multi-scale entanglement renormalization ansatz (MERA) generates a (D+1)-dimensional holographic geometry. Here we focus on homogeneous tensor networks, where all the tensors in the network are copies of the same tensor, and argue that certain structural properties of the resulting many-body states are preconditioned by the geometry of the tensor network and are therefore largely independent of the choice of variational parameters. Indeed, the asymptotic decay of correlations in homogeneous MPS and MERA for D=1 systems is seen to be determined by the structure of geodesics in the physical and holographic geometries, respectively; whereas the asymptotic scaling of entanglement entropy is seen to always obey a simple boundary law -- that is, again in the relevant geometry. This geometrical interpretation offers a simple and unifying framework to understand the structural properties of, and helps clarify the relation between, different tensor network states. In addition, it has recently motivated the branching MERA, a generalization of the MERA capable of reproducing violations of the entropic boundary law in D>1 dimensions.Comment: 18 pages, 18 figure

Exact and simple results for the XYZ and strongly interacting fermion chains

We conjecture exact and simple formulas for physical quantities in two quantum chains. A classic result of this type is Onsager, Kaufman and Yang's formula for the spontaneous magnetization in the Ising model, subsequently generalized to the chiral Potts models. We conjecture that analogous results occur in the XYZ chain when the couplings obey J_xJ_y + J_yJ_z + J_x J_z=0, and in a related fermion chain with strong interactions and supersymmetry. We find exact formulas for the magnetization and gap in the former, and the staggered density in the latter, by exploiting the fact that certain quantities are independent of finite-size effects