Obtaining highly-excited eigenstates of many-body localized Hamiltonians by the density matrix renormalization group

The eigenstates of many-body localized (MBL) Hamiltonians exhibit low entanglement. We adapt the highly successful density-matrix renormalization group method, which is usually used to find modestly entangled ground states of local Hamiltonians, to find individual highly excited eigenstates of many body localized Hamiltonians. The adaptation builds on the distinctive spatial structure of such eigenstates. We benchmark our method against the well studied random field Heisenberg model in one dimension. At moderate to large disorder, we find that the method successfully obtains excited eigenstates with high accuracy, thereby enabling a study of MBL systems at much larger system sizes than those accessible to exact-diagonalization methods.Comment: Published version. Slightly expanded discussion; supplement adde

fMRI reveals a common neural substrate of illusory and real contours in V1 after perceptual learning

Perceptual learning involves the specific and relatively permanent modification of perception following a sensory experience. In psychophysical experiments, the specificity of the learning effects to the trained stimulus attributes (e.g., visual field position or stimulus orientation) is often attributed to assumed neural modifications at an early cortical site within the visual processing hierarchy. We directly investigated a neural correlate of perceptual learning in the primary visual cortex using fMRI. Twenty volunteers practiced a curvature discrimination on Kanizsa-type illusory contours in the MR scanner. Practice-induced changes in the BOLD response to illusory contours were compared between the pretraining and the posttraining block in those areas of the primary visual cortex (V1) that, in the same session, had been identified to represent real contours at corresponding visual field locations. A retinotopically specific BOLD signal increase to illusory contours was observed as a consequence of the training, possibly signaling the formation of a contour representation, which is necessary for performing the curvature discrimination. The effects of perceptual training were maintained over a period of about 10 months, and they were specific to the trained visual field position. The behavioral specificity of the learning effects supports an involvement of V1 in perceptual learning, and not in unspecific attentional effects

Bound states and E_8 symmetry effects in perturbed quantum Ising chains

In a recent experiment on CoNb_2O_6, Coldea et al. [Science 327, 177 (2010)] found for the first time experimental evidence of the exceptional Lie algebra E_8. The emergence of this symmetry was theoretically predicted long ago for the transverse quantum Ising chain in the presence of a weak longitudinal field. We consider an accurate microscopic model of CoNb_2O_6 incorporating additional couplings and calculate numerically the dynamical structure function using a recently developed matrix-product-state method. The excitation spectra show bound states characteristic of the weakly broken E_8 symmetry. We compare the observed bound state signatures in this model to those found in the transverse Ising chain in a longitudinal field and to experimental data.Comment: 4 pages, 3 figure

Infinite density matrix renormalization group for multicomponent quantum Hall systems

While the simplest quantum Hall plateaus, such as the $\nu = 1/3$ state in GaAs, can be conveniently analyzed by assuming only a single active Landau level participates, for many phases the spin, valley, bilayer, subband, or higher Landau level indices play an important role. These `multi-component' problems are difficult to study using exact diagonalization because each component increases the difficulty exponentially. An important example is the plateau at $\nu = 5/2$, where scattering into higher Landau levels chooses between the competing non-Abelian Pfaffian and anti-Pfaffian states. We address the methodological issues required to apply the infinite density matrix renormalization group to quantum Hall systems with multiple components and long-range Coulomb interactions, greatly extending accessible system sizes. As an initial application we study the problem of Landau level mixing in the $\nu = 5/2$ state. Within the approach to Landau level mixing used here, we find that at the Coulomb point the anti-Pfaffian is preferred over the Pfaffian state over a range of Landau level mixing up to the experimentally relevant values.Comment: 12 pages, 9 figures. v2 added more data for different amounts of Landau level mixing at 5/2 fillin

Time-evolving a matrix product state with long-ranged interactions

We introduce a numerical algorithm to simulate the time evolution of a matrix product state under a long-ranged Hamiltonian. In the effectively one-dimensional representation of a system by matrix product states, long-ranged interactions are necessary to simulate not just many physical interactions but also higher-dimensional problems with short-ranged interactions. Since our method overcomes the restriction to short-ranged Hamiltonians of most existing methods, it proves particularly useful for studying the dynamics of both power-law interacting one-dimensional systems, such as Coulombic and dipolar systems, and quasi two-dimensional systems, such as strips or cylinders. First, we benchmark the method by verifying a long-standing theoretical prediction for the dynamical correlation functions of the Haldane-Shastry model. Second, we simulate the time evolution of an expanding cloud of particles in the two-dimensional Bose-Hubbard model, a subject of several recent experiments.Comment: 5 pages + 3 pages appendices, 4 figure

Lecithin addition to starter pig diets with and without added fat and whey

A total of 316 crossbred weanling pigs were used in two studies to evaluate the effect of the addition of edible-grade, unbleached soy lecithin on growth in starter pig diets with and without added fat and/or dried whey. Addition of fat to a corn-soybean meal diet improved (P\u3c.05) feed efficiency but addition of lecithin did not affect performance. When lecithin and fat were added in combination, average daily gain was less (P\u3c.05) than for diets without added fat. This may be due to a high level of undigestible fat having a limiting effect on intake and consequently decreasing gains. A low level of lecithin (1.5%) in diets without whey gave approximately the same response as a 4% fat diet without thus making lecithin a possible fat substitute should, it be economically feasible.; Swine Day, Manhattan, KS, November 15, 198