Fast convergence of imaginary time evolution tensor network algorithms by recycling the environment

We propose an environment recycling scheme to speed up a class of tensor network algorithms that produce an approximation to the ground state of a local Hamiltonian by simulating an evolution in imaginary time. Specifically, we consider the time-evolving block decimation (TEBD) algorithm applied to infinite systems in 1D and 2D, where the ground state is encoded, respectively, in a matrix product state (MPS) and in a projected entangled-pair state (PEPS). An important ingredient of the TEBD algorithm (and a main computational bottleneck, especially with PEPS in 2D) is the computation of the so-called environment, which is used to determine how to optimally truncate the bond indices of the tensor network so that their dimension is kept constant. In current algorithms, the environment is computed at each step of the imaginary time evolution, to account for the changes that the time evolution introduces in the many-body state represented by the tensor network. Our key insight is that close to convergence, most of the changes in the environment are due to a change in the choice of gauge in the bond indices of the tensor network, and not in the many-body state. Indeed, a consistent choice of gauge in the bond indices confirms that the environment is essentially the same over many time steps and can thus be re-used, leading to very substantial computational savings. We demonstrate the resulting approach in 1D and 2D by computing the ground state of the quantum Ising model in a transverse magnetic field.Comment: 17 pages, 28 figure

Simulation of anyons with tensor network algorithms

Interacting systems of anyons pose a unique challenge to condensed matter simulations due to their non-trivial exchange statistics. These systems are of great interest as they have the potential for robust universal quantum computation, but numerical tools for studying them are as yet limited. We show how existing tensor network algorithms may be adapted for use with systems of anyons, and demonstrate this process for the 1-D Multi-scale Entanglement Renormalisation Ansatz (MERA). We apply the MERA to infinite chains of interacting Fibonacci anyons, computing their scaling dimensions and local scaling operators. The scaling dimensions obtained are seen to be in agreement with conformal field theory. The techniques developed are applicable to any tensor network algorithm, and the ability to adapt these ansaetze for use on anyonic systems opens the door for numerical simulation of large systems of free and interacting anyons in one and two dimensions.Comment: Fixed typos, matches published version. 16 pages, 21 figures, 4 tables, RevTeX 4-1. For a related work, see arXiv:1006.247

Dynamical windows for real-time evolution with matrix product states

We propose the use of a dynamical window to investigate the real-time evolution of quantum many-body systems in a one-dimensional lattice. In a recent paper [H. Phien et al, arxiv:????.????], we introduced infinite boundary conditions (IBC) in order to investigate real-time evolution of an infinite system under a local perturbation. This was accomplished by restricting the update of the tensors in the matrix product state to a finite window, with left and right boundaries held at fixed positions. Here we consider instead the use of a dynamical window, namely a window where the positions of left and right boundaries are allowed to change in time. In this way, all simulation efforts can be devoted to the space-time region of interest, which leads to a remarkable reduction in computational costs. For illustrative purposes, we consider two applications in the context of the spin-1 antiferromagnetic Heisenberg model in an infinite spin chain: one is an expanding window, with boundaries that are adjusted to capture the expansion in time of a local perturbation of the system; the other is a moving window of fixed size, where the position of the window follows the front of a propagating wave

Prevalence and determinants of weight misperception in an urban Swiss population.

Weight misperception precludes effective management of pre-obesity and obesity, but little is known regarding its status in the Swiss population. Our study aimed to assess the prevalence and determinants of weight over- and underestimation in an adult urban Swiss population. Cross-sectional study conducted between 2009 and 2012 in the city of Lausanne. Height and weight were measured using standardised procedures. Weight perception and other socio-demographic variables were collected through questionnaires. Data from 4284 participants (2261 women, 57.5 ± 10.4 years) were analysed. Overall, almost one-fifth (18%) of participants underestimated their weight, while only 7% overestimated it. One quarter of women and half of men with overweight underestimated their weight; the corresponding values for obese subjects were 7% and 10%. Multivariate analysis showed male gender (odds ratio [OR] 3.09, 95% confidence interval [CI] 2.54-3.76), increasing age or body mass index (p-value for trend <0.001), being born in Portugal (OR 2.10, 95% CI 1.42-3.10), low education (OR 1.90, 95% CI 1.47-2.47), and absence of diagnosis of pre-obesity or obesity by the doctor (OR 5.61, 95% CI 4.51-7.00) to be associated with weight underestimation. Overestimation was significantly higher in women (19.6%) than in men (8.5%). Weight overestimation was negatively associated with male gender (OR 0.29, 95% CI 0.22-0.39), increasing age (p-value for trend <0.001), being born in Portugal (OR 0.37, 95% CI 0.16-0.87) and positively associated with absence of diagnosis (OR 3.11, 95% CI 2.23-4.34). Almost one quarter of the Swiss population aged 40 to 80 has weight misperception, underestimation being over twice as frequent as overestimation. Adequate diagnosis of overweight or obesity might be the best deterrent against weight misperception

Infinite boundary conditions for matrix product state calculations

We propose a formalism to study dynamical properties of a quantum many-body system in the thermodynamic limit by studying a finite system with infinite boundary conditions (IBC) where both finite size effects and boundary effects have been eliminated. For one-dimensional systems, infinite boundary conditions are obtained by attaching two boundary sites to a finite system, where each of these two sites effectively represents a semi-infinite extension of the system. One can then use standard finite-size matrix product state techniques to study a region of the system while avoiding many of the complications normally associated with finite-size calculations such as boundary Friedel oscillations. We illustrate the technique with an example of time evolution of a local perturbation applied to an infinite (translationally invariant) ground state, and use this to calculate the spectral function of the S=1 Heisenberg spin chain. This approach is more efficient and more accurate than conventional simulations based on finite-size matrix product state and density-matrix renormalization-group approaches.Comment: 10 page

Characterization of non-local gates

A non-local unitary transformation of two qubits occurs when some Hamiltonian interaction couples them. Here we characterize the amount, as measured by time, of interaction required to perform two--qubit gates, when also arbitrarily fast, local unitary transformations can be applied on each qubit. The minimal required time of interaction, or interaction cost, defines an operational notion of the degree of non--locality of gates. We characterize a partial order structure based on this notion. We also investigate the interaction cost of several communication tasks, and determine which gates are able to accomplish them. This classifies two--qubit gates into four categories, differing in their capability to transmit classical, as well as quantum, bits of information.Comment: revtex, 14 pages, no pictures; proof of result 1 simplified significantl

Entanglement renormalization, scale invariance, and quantum criticality

The use of entanglement renormalization in the presence of scale invariance is investigated. We explain how to compute an accurate approximation of the critical ground state of a lattice model, and how to evaluate local observables, correlators and critical exponents. Our results unveil a precise connection between the multi-scale entanglement renormalization ansatz (MERA) and conformal field theory (CFT). Given a critical Hamiltonian on the lattice, this connection can be exploited to extract most of the conformal data of the CFT that describes the model in the continuum limit.Comment: 4 pages, 3 figures, RevTeX 4. Revised for greater clarit

Iron metabolism and incidence of metabolic syndrome.

BACKGROUND AND AIMS: Whether iron metabolism affects metabolic syndrome (METS) is debated. We assessed the association between several markers of iron metabolism and incidence of METS. METHODS AND RESULTS: Data from 3271 participants (1870 women, 51.3 ± 10.4 years), free of METS at baseline and followed for 5.5 years. The association of serum iron, ferritin and transferrin with incident METS was assessed separately by gender. Incidence of METS was 22.6% in men and 16.5% in women (p < 0.001). After multivariate adjustment, a positive association was found between transferrin and incident METS in men: odds ratio (OR) and 95% confidence interval for the fourth relative to the first quartile 1.55 (1.04-2.31), p for trend = 0.03, while no association was found for iron OR = 0.81 (0.53-1.24), p for trend = 0.33 and ferritin OR = 1.30 (0.88-1.92), p for trend = 0.018. In women, a negative association was found between iron and incident METS: OR for the fourth relative to the first quartile 0.51 (0.33-0.80), p for trend<0.03; the association between transferrin and incident METS was borderline significant: OR = 1.45 (0.97-2.17), p for trend = 0.07 and no association was found for ferritin: OR = 1.11 (0.76-1.63), p for trend = 0.58. CONCLUSION: Transferrin, not ferritin, is independently associated with an increased risk of incident METS; the protective effect of iron in women should be further explored

Boundary quantum critical phenomena with entanglement renormalization

We extend the formalism of entanglement renormalization to the study of boundary critical phenomena. The multi-scale entanglement renormalization ansatz (MERA), in its scale invariant version, offers a very compact approximation to quantum critical ground states. Here we show that, by adding a boundary to the scale invariant MERA, an accurate approximation to the critical ground state of an infinite chain with a boundary is obtained, from which one can extract boundary scaling operators and their scaling dimensions. Our construction, valid for arbitrary critical systems, produces an effective chain with explicit separation of energy scales that relates to Wilson's RG formulation of the Kondo problem. We test the approach by studying the quantum critical Ising model with free and fixed boundary conditions.Comment: 8 pages, 12 figures, for a related work see arXiv:0912.289