Simulation of strongly correlated fermions in two spatial dimensions with fermionic Projected Entangled-Pair States

We explain how to implement, in the context of projected entangled-pair states (PEPS), the general procedure of fermionization of a tensor network introduced in [P. Corboz, G. Vidal, Phys. Rev. B 80, 165129 (2009)]. The resulting fermionic PEPS, similar to previous proposals, can be used to study the ground state of interacting fermions on a two-dimensional lattice. As in the bosonic case, the cost of simulations depends on the amount of entanglement in the ground state and not directly on the strength of interactions. The present formulation of fermionic PEPS leads to a straightforward numerical implementation that allowed us to recycle much of the code for bosonic PEPS. We demonstrate that fermionic PEPS are a useful variational ansatz for interacting fermion systems by computing approximations to the ground state of several models on an infinite lattice. For a model of interacting spinless fermions, ground state energies lower than Hartree-Fock results are obtained, shifting the boundary between the metal and charge-density wave phases. For the t-J model, energies comparable with those of a specialized Gutzwiller-projected ansatz are also obtained.Comment: 25 pages, 35 figures (revised version

AReS and MaRS - Adversarial and MMD-Minimizing Regression for SDEs

Stochastic differential equations are an important modeling class in many disciplines. Consequently, there exist many methods relying on various discretization and numerical integration schemes. In this paper, we propose a novel, probabilistic model for estimating the drift and diffusion given noisy observations of the underlying stochastic system. Using state-of-the-art adversarial and moment matching inference techniques, we avoid the discretization schemes of classical approaches. This leads to significant improvements in parameter accuracy and robustness given random initial guesses. On four established benchmark systems, we compare the performance of our algorithms to state-of-the-art solutions based on extended Kalman filtering and Gaussian processes.Comment: Published at the Thirty-sixth International Conference on Machine Learning (ICML 2019

Three-sublattice order in the SU(3) Heisenberg model on the square and triangular lattice

We present a numerical study of the SU(3) Heisenberg model of three-flavor fermions on the triangular and square lattice by means of the density-matrix renormalization group (DMRG) and infinite projected entangled-pair states (iPEPS). For the triangular lattice we confirm that the ground state has a three-sublattice order with a finite ordered moment which is compatible with the result from linear flavor wave theory (LFWT). The same type of order has recently been predicted also for the square lattice [PRL 105, 265301 (2010)] from LFWT and exact diagonalization. However, for this case the ordered moment cannot be computed based on LFWT due to divergent fluctuations. Our numerical study clearly supports this three-sublattice order, with an ordered moment of m=0.2-0.4 in the thermodynamic limit.Comment: Published version. 11 pages, 6 figure

Harmonic generation by atoms in circularly polarized two-color laser fields with coplanar polarizations and commensurate frequencies

The generation of harmonics by atoms or ions in a two-color, coplanar field configuration with commensurate frequencies is investigated through both, an analytical calculation based on the Lewenstein model and the numerical ab initio solution of the time-dependent Schroedinger equation of a two-dimensional model ion. Through the analytical model, selection rules for the harmonic orders in this field configuration, a generalized cut-off for the harmonic spectra, and an integral expression for the harmonic dipole strength is provided. The numerical results are employed to test the predictions of the analytical model. The scaling of the cut-off as a function of both, one of the laser intensities and frequency ratio $\eta$, as well as entire spectra for different $\eta$ and laser intensities are presented and analyzed. The theoretical cut-off is found to be an upper limit for the numerical results. Other discrepancies between analytical model and numerical results are clarified by taking into account the probabilities of the absorption processes involved.Comment: 8 figure

Mechanical behavior and size effects of polymer/amorphous NiB composites with 3D micro‐ architectures

Micro-architectured materials are a new class of hierarchical cellular material with outstanding properties. By designing advantageous cellular geometries and combining the material size effects at the nanometer scale, lightweight hybrid micro-architectured materials with hierarchical cellular structures and tailored structural properties are achieved. Previous papers have reported the mechanical properties of ceramic/polymer composites but few studies have examined the properties of similar structures with metal coatings instead of ceramic. To estimate the mechanical performance of polymer cellular structure reinforced with a metal coating, we combined 3D laser lithography and electroless deposition of an amorphous layer of NiB to produce metal/polymer hybrid structures. In this poster, the fabrication of 3D hybrid structures by electroless deposition aiming at achieving high and yet low density material will be presented. We also studied the mechanical response of micro-architectured structures as a function of the architecture design and the thickness of the amorphous NiB layer on their deformation mechanisms. In situ SEM microcompression experiments revealed a change in the deformation behavior with the NiB layer thickness, suggesting that the deformation mechanism and the buckling behavior are controlled by the size induced brittle-to-ductile transition in the NiB layer. In addition, the energy absorption properties demonstrate the possibility of tuning the energy absorption efficiency with adequate designs. Please click Additional Files below to see the full abstract

Plasma exchange in the intensive care unit: a narrative review

In this narrative review, we discuss the relevant issues of therapeutic plasma exchange (TPE) in critically ill patients. For many conditions, the optimal indication, device type, frequency, duration, type of replacement fluid and criteria for stopping TPE are uncertain. TPE is a potentially lifesaving but also invasive procedure with risk of adverse events and complications and requires close monitoring by experienced teams. In the intensive care unit (ICU), the indications for TPE can be divided into (1) absolute, well-established, and evidence-based, for which TPE is recognized as first-line therapy, (2) relative, for which TPE is a recognized second-line treatment (alone or combined) and (3) rescue therapy, where TPE is used with a limited or theoretical evidence base. New indications are emerging and ongoing knowledge gaps, notably regarding the use of TPE during critical illness, support the establishment of a TPE registry dedicated to intensive care medicine

Along the Spectrum of Women\u27s Rights Advocacy: A Cross-Cultural Comparison of Sexual Harassment Law in the United States and India

This Comment compares the development of sexual harassment law in the United States and India. It strives to contribute to this global feminist debate by highlighting the successes and failures of each country\u27s respective anti-harassment protections. It also compares the United States\u27 and India\u27s legal approaches to the problem of workplace sexual harassment. The Comment also discusses the successes and failures of the U.S. and Indian protections in a manner that attempts to minimize the problems present in cross-cultural studies