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Testing autonomous robotic manipulators is challenging due to the complex software interactions between vision and control components. A crucial element of modern robotic manipulators is the deep learning based object detection model. The creation and assessment of this model requires real world data, which can be hard to label and collect, especially when the hardware setup is not available. The current techniques primarily focus on using synthetic data to train deep neural networks (DDNs) and identifying failures through offline or online simulation-based testing. However, the process of exploiting the identified failures to uncover design flaws early on, and leveraging the optimized DNN within the simulation to accelerate the engineering of the DNN for real-world tasks remains unclear. To address these challenges, we propose the MARTENS (Manipulator Robot Testing and Enhancement in Simulation) framework, which integrates a photorealistic NVIDIA Isaac Sim simulator with evolutionary search to identify critical scenarios aiming at improving the deep learning vision model and uncovering system design flaws. Evaluation of two industrial case studies demonstrated that MARTENS effectively reveals robotic manipulator system failures, detecting 25 % to 50 % more failures with greater diversity compared to random test generation. The model trained and repaired using the MARTENS approach achieved mean average precision (mAP) scores of 0.91 and 0.82 on real-world images with no prior retraining. Further fine-tuning on real-world images for a few epochs (less than 10) increased the mAP to 0.95 and 0.89 for the first and second use cases, respectively. In contrast, a model trained solely on real-world data achieved mAPs of 0.8 and 0.75 for use case 1 and use case 2 after more than 25 epochs.

We generalize conventional multiferroicity \ -- simultaneous existence of ferroelectric and ferromagnetic orders \ -- to multipolar degrees of freedom, examining its emergence in a $d^2$ Mott insulator with strong spin-orbit and Hund's couplings. Specifically, we investigate the origin of magnetic multipolar interactions in $d^2$ Mott insulators. In addition, we show that an admixture of quadrupolar and octupolar magnetic order simultaneously induces electrical quadrupolar and ferroelectric polarization. Our theoretical formalism extends the multiferroic framework to the higher-order sector, exploring the possibility of coexisting multipolar orders of the same and different ranks. We finally comment on some of the experimental signatures., Comment: 5+12 pages, 7 figures, comments are welcome

In this paper, we show that the diffraction of the primes is absolutely continuous, showing no bright spots (Bragg peaks). We introduce the notion of counting diffraction, extending the classical notion of (density) diffraction to sets of density zero. We develop the counting diffraction theory and give many examples of sets of zero density of all possible spectral types., Comment: 33 pages

We characterize inclusions of compact noncommutative convex sets with the property that every continuous affine function on the smaller set can be extended to a continuous affine function on the larger set with a uniform bound. As an application of this result, we obtain a simple geometric characterization of (possibly nonunital) operator systems that are dualizable, meaning that their dual can be equipped with an operator system structure. We further establish some permanence properties of dualizability, and provide a large new class of dualizable operator systems. These results are new even when specialized to ordinary compact convex sets.

The presence of competing interactions due to geometry leads to frustration in quantum spin models. As a consequence, the ground state of such systems often displays a large degeneracy that can be lifted due to thermal or quantum effects. One such example is the antiferromagnetic Ising model on the Kagome lattice. It was shown that while the same model on the triangular lattice is ordered at zero temperature for small transverse field due to an order by disorder mechanism, the Kagome lattice resists any such effects and exhibits only short range spin correlations and a trivial paramagnetic phase. We embed this model on the latest architecture of D-Wave's quantum annealer, the Advantage2 prototype, which uses the highly connected Zephyr graph. Using advanced embedding and calibration techniques, we are able to embed a Kagome lattice with mixed open and periodic boundary conditions of 231 sites on the full graph of the currently available prototype. Through forward annealing experiments, we show that under a finite longitudinal field the system exhibits a one-third magnetization plateau, consistent with a classical spin liquid state of reduced entropy. An anneal-pause-quench protocol is then used to extract an experimental ensemble of states resulting from the equilibration of the model at finite transverse and longitudinal field. This allows us to construct a partial phase diagram and confirm that the system exits the constrained Hilbert space of the classical spin liquid when subjected to a transverse field. We connect our results to previous theoretical results and quantum Monte Carlo simulation, which helps us confirm the validity of the quantum simulation realized here, thereby extracting insight into the performance of the D-Wave quantum annealer to simulate non-trivial quantum systems in equilibrium., Comment: 12 + 6 pages, 7 + 8 figures, updated paper to be published in PRB

Context: Machine Learning (ML) is integrated into a growing number of systems for various applications. Because the performance of an ML model is highly dependent on the quality of the data it has been trained on, there is a growing interest in approaches to detect and repair data errors (i.e., data cleaning). Researchers are also exploring how ML can be used for data cleaning; hence creating a dual relationship between ML and data cleaning. To the best of our knowledge, there is no study that comprehensively reviews this relationship. Objective: This paper's objectives are twofold. First, it aims to summarize the latest approaches for data cleaning for ML and ML for data cleaning. Second, it provides future work recommendations. Method: We conduct a systematic literature review of the papers published between 2016 and 2022 inclusively. We identify different types of data cleaning activities with and for ML: feature cleaning, label cleaning, entity matching, outlier detection, imputation, and holistic data cleaning. Results: We summarize the content of 101 papers covering various data cleaning activities and provide 24 future work recommendations. Our review highlights many promising data cleaning techniques that can be further extended. Conclusion: We believe that our review of the literature will help the community develop better approaches to clean data., Comment: Published in the Automated Software Engineering Journal

In this paper, we show that the semi-Dirichlet C*-covers of a semi-Dirichlet operator algebra form a complete lattice, establishing that there is a maximal semi-Dirichlet C*-cover. Given an operator algebra dynamical system we prove a dilation theory that shows that the full crossed product is isomorphic to the relative full crossed product with respect to this maximal semi-Dirichlet cover. In this way, we can show that every semi-Dirichlet dynamical system has a semi-Dirichlet full crossed product.

Evolutionary search-based techniques are commonly used for testing autonomous robotic systems. However, these approaches often rely on computationally expensive simulator-based models for test scenario evaluation. To improve the computational efficiency of the search-based testing, we propose augmenting the evolutionary search (ES) with a reinforcement learning (RL) agent trained using surrogate rewards derived from domain knowledge. In our approach, known as RIGAA (Reinforcement learning Informed Genetic Algorithm for Autonomous systems testing), we first train an RL agent to learn useful constraints of the problem and then use it to produce a certain part of the initial population of the search algorithm. By incorporating an RL agent into the search process, we aim to guide the algorithm towards promising regions of the search space from the start, enabling more efficient exploration of the solution space. We evaluate RIGAA on two case studies: maze generation for an autonomous ant robot and road topology generation for an autonomous vehicle lane keeping assist system. In both case studies, RIGAA converges faster to fitter solutions and produces a better test suite (in terms of average test scenario fitness and diversity). RIGAA also outperforms the state-of-the-art tools for vehicle lane keeping assist system testing, such as AmbieGen and Frenetic.

In this paper it is shown that the lattice of C*-covers of an operator algebra does not contain enough information to distinguish operator algebras up to completely isometric isomorphism. In addition, four natural equivalences of the lattice of C*-covers are developed and proven to be distinct. The lattice of C*-covers of direct sums and tensor products are studied. Along the way key examples are found of an operator algebra that generates exactly n C*-algebras up to *-isomorphism and a simple operator algebra that is not similar to a C*-algebra., Comment: Accepted to the Canadian Journal of Mathematics

Thorough testing of safety-critical autonomous systems, such as self-driving cars, autonomous robots, and drones, is essential for detecting potential failures before deployment. One crucial testing stage is model-in-the-loop testing, where the system model is evaluated by executing various scenarios in a simulator. However, the search space of possible parameters defining these test scenarios is vast, and simulating all combinations is computationally infeasible. To address this challenge, we introduce AmbieGen, a search-based test case generation framework for autonomous systems. AmbieGen uses evolutionary search to identify the most critical scenarios for a given system, and has a modular architecture that allows for the addition of new systems under test, algorithms, and search operators. Currently, AmbieGen supports test case generation for autonomous robots and autonomous car lane keeping assist systems. In this paper, we provide a high-level overview of the framework's architecture and demonstrate its practical use cases., Comment: 17 pages, 10 figures

Direct sampling from a Slater determinant is combined with an autoregressive deep neural network as a Jastrow factor into a fully autoregressive Slater-Jastrow ansatz for variational quantum Monte Carlo, which allows for uncorrelated sampling. The elimination of the autocorrelation time leads to a stochastic algorithm with provable cubic scaling (with a potentially large prefactor), i.e. the number of operations for producing an uncorrelated sample and for calculating the local energy scales like $\mathcal{O}(N_s^3)$ with the number of orbitals $N_s$. The implementation is benchmarked on the two-dimensional $t-V$ model of spinless fermions on the square lattice., Comment: 60 pages; Submission to SciPost

Many modern cyber physical systems incorporate computer vision technologies, complex sensors and advanced control software, allowing them to interact with the environment autonomously. Testing such systems poses numerous challenges: not only should the system inputs be varied, but also the surrounding environment should be accounted for. A number of tools have been developed to test the system model for the possible inputs falsifying its requirements. However, they are not directly applicable to autonomous cyber physical systems, as the inputs to their models are generated while operating in a virtual environment. In this paper, we aim to design a search based framework, named AmbieGen, for generating diverse fault revealing test scenarios for autonomous cyber physical systems. The scenarios represent an environment in which an autonomous agent operates. The framework should be applicable to generating different types of environments. To generate the test scenarios, we leverage the NSGA II algorithm with two objectives. The first objective evaluates the deviation of the observed system behaviour from its expected behaviour. The second objective is the test case diversity, calculated as a Jaccard distance with a reference test case. We evaluate AmbieGen on three scenario generation case studies, namely a smart-thermostat, a robot obstacle avoidance system, and a vehicle lane keeping assist system. We compared three configurations of AmbieGen: based on a single objective genetic algorithm, multi objective, and random search. Both single and multi objective configurations outperform the random search. Multi objective configuration can find the individuals of the same quality as the single objective, producing more unique test scenarios in the same time budget.

Consumer grade cyber-physical systems (CPS) are becoming an integral part of our life, automatizing and simplifying everyday tasks. Indeed, due to complex interactions between hardware, networking and software, developing and testing such systems is known to be a challenging task. Various quality assurance and testing strategies have been proposed. The most common approach for pre-deployment testing is to model the system and run simulations with models or software in the loop. In practice, most often, tests are run for a small number of simulations, which are selected based on the engineers' domain knowledge and experience. In this paper we propose an approach to automatically generate fault-revealing test cases for CPS. We have implemented our approach in Python, using standard frameworks and used it to generate scenarios violating temperature constraints for a smart thermostat implemented as a part of our IoT testbed. Data collected from an application managing a smart building have been used to learn models of the environment under ever changing conditions. The suggested approach allowed us to identify several pit-fails, scenarios (i.e., environment conditions and inputs), where the system behaves not as expected., Comment: 4 pages, to be published in SBST2021 workshop proceedings

Classically, Jensen's Inequality asserts that if $X$ is a compact convex set, and $f:K\to \mathbb{R}$ is a convex function, then for any probability measure $\mu$ on $K$, that $f(\text{bar}(\mu))\le \int f\;d\mu$, where $\text{bar}(\mu)$ is the barycenter of $\mu$. Recently, Davidson and Kennedy proved a noncommutative ("nc") version of Jensen's inequality that applies to nc convex functions, which take matrix values, with probability measures replaced by ucp maps. In the classical case, if $f$ is only a separately convex function, then $f$ still satisfies the Jensen inequality for any probability measure which is a product measure. We prove a noncommutative Jensen inequality for functions which are separately nc convex in each variable. The inequality holds for a large class of ucp maps which satisfy a noncommutative analogue of Fubini's theorem. This class of ucp maps includes any free product of ucp maps built from Boca's theorem, or any ucp map which is conditionally free in the free-probabilistic sense of M{\l}otkowski. As an application to free probability, we obtain some operator inequalities for conditionally free ucp maps applied to free semicircular families., Comment: 24 pages

A variety of goods and services in the contemporary world requires permanent improvement of services e-commerce platform performance. Modern society is so deeply integrated with mail deliveries, purchasing of goods and services online, that makes competition between service and good providers a key selection factor. As long as logistic, timely, and cost-effective delivery plays important part authors decided to analyze possible ways of improvements in the current field, especially for regions distantly located from popular distribution centers. Considering both: fast and lazy delivery the factor of costs is playing an important role for each end-user. Given work proposes a simulation that analyses the current cost of delivery for e-commerce orders in the context of delivery by the Supplier Fleet, World-Wide delivery service fleet, and possible vendor drop-ship and checks of the alternative ways can be used to minimize the costs. The main object of investigation is focused around mid and small businesses living far from big distribution centers (except edge cases like lighthouses, edge rocks with very limited accessibility) but actively using e-commerce solutions for daily activities fulfillment. Authors analyzed and proposed a solution for the problem of cost optimization for packages delivery for long-distance deliveries using a combination of paths delivered by supplier fleets, worldwide and local carriers. Data models and Add-ons of contemporary Enterprise Resource Planning systems were used, and additional development is proposed in the perspective of the flow selection change. The experiment is based on data sources of the United States companies using a wide range of carriers for delivery services and uses the data sources of the real companies; however, it applies repetitive simulations to analyze variances in obtained solutions.

A numerical method is presented for reproducing fermionic quantum gas microscope experiments in equilibrium. By employing nested componentwise direct sampling of fermion pseudo-density matrices, as they arise naturally in determinantal quantum Monte Carlo (QMC) simulations, a stream of pseudo-snapshots of occupation numbers on large systems can be produced. There is a sign problem even when the conventional determinantal QMC algorithm can be made sign-problem free, and every pseudo-snapshot comes with a sign and a reweighting factor. Nonetheless, this "sampling sign problem" turns out to be weak and manageable in a large, relevant parameter regime. The method allows to compute distribution functions of arbitrary quantities defined in occupation number space and, from a practical point of view, facilitates the computation of complicated conditional correlation functions. While the projective measurements in quantum gas microscope experiments achieve direct sampling of occupation number states from the density matrix, the presented numerical method requires a Markov chain as an intermediate step and thus achieves only indirect sampling, but the full distribution of pseudo-snapshots after (signed) reweighting is identical to the distribution of snapshots from projective measurements, Comment: 5 + 10 pages, 3 + 8 figures, including link to program code, published version

For the inverse square long-range ferromagnetic Ising chain in a transverse field, the thermal phase boundary of the floating Kosterlitz-Thouless phase is obtained for several values of the transverse field down to the quantum critical point. The sharp domain walls in the classical model are increasingly smeared out by the transverse field, which is evidenced by a pronounced broadening of the non-universal bump in the specific heat. The discernability of KT critical scaling in finite-size simulations is discussed., Comment: 11 pages, 9 figures

A semicrossed product is a non-selfadjoint operator algebra encoding the action of a semigroup on an operator or C*-algebra. We prove that, when the positive cone of a discrete lattice ordered abelian group acts on a C*-algebra, the C*-envelope of the associated semicrossed product is a full corner of a crossed product by the whole group. By constructing a C*-cover that itself is a full corner of a crossed product, and computing the Shilov ideal, we obtain an explicit description of the C*-envelope. This generalizes a result of Davidson, Fuller, and Kakariadis from $\mathbb{Z}_+^n$ to the class of all discrete lattice ordered abelian groups., Comment: 36 pages. Updated to reflect published version in JFA. Minor typos fixed throughout and new Corollary 3.18 (nonunital case) and Subsection 6.1 (simplicity of the C*-envelope) added

Complex magnetic orders in frustrated magnets may exhibit rich melting processes when the magnet is heated toward the paramagnetic phase. We show that one may tune such melting processes by quantum fluctuations. We consider a kagome lattice dipolar Ising model subject to transverse field and focus on the thermal transitions out of its magnetic ground state, which features a $\sqrt{3}\times\sqrt{3}$ magnetic unit cell. Our quantum Monte Carlo (QMC) simulations suggest that, at weak transverse field, the $\sqrt{3}\times\sqrt{3}$ phase melts by way of an intermediate magnetic charge ordered phase where the lattice translation symmetry is restored while the time reversal symmetry remains broken. By contrast, at stronger transverse field, QMC simulations suggest the $\sqrt{3}\times\sqrt{3}$ phase melts through a floating Kosterlitz-Thouless phase. The two distinct melting processes are separated by either a multicritical point or a short line of first order phase transition., Comment: 13 pages, 8 figures; minor revisions

In this study, two different simple and intuitive semiempirical schemes for computing approximate non-adiabatic coupling vectors (NACVs) between the ground and excited electronic states are presented. The first approximation makes use of Mulliken transition charges, while the second is based on derivative coupling vectors between localized molecular orbitals. Both approximations lend themselves easily to implementation within a whole spectrum of semiempirical quantum-chemical semiempirical methods. Here we present the implementation within the tight-binding DFT and benchmark its performance against analytical TD-DFT NAC vectors for a range of planar fluorescent chromophores at the Franck-Condon point. The pattern of the atomic NAC vectors is often reproduced, but the relative magnitude and total length of the NAC vector are often in serious error. Although quantitative predictions are not possible, these simple and intuitive approximations allow to explain, in a qualitative way, trends in the electronic coupling in extended molecular systems and complex materials. In this context, we investigate how the non-adiabatic coupling depends on the delocalization length of an excitation in chromophoric oligomers based on a simple model. Finally, we make general qualitative predictions on the size dependence of the fluorescence quantum yields in extended molecular systems, and illustrate those on the example of triply fused porphyrin tapes with increasing length.

Motivated by recent quantum gas microscope experiments for fermions in optical lattices, we present proof of principle calculations showing that it is possible to obtain the complete information about the quantum state on a small subsystem from equilibrium determinantal quantum Monte Carlo simulations. Both diagonal (in the occupation number basis) and off-diagonal elements of the reduced density matrix are calculated for a square plaquette, which is embedded in a much larger system of the two-dimensional Hubbard model, both at half filling and in the doped case. The diagonalization of the reduced density matrix is done by exploiting the point group symmetry and particle number conservation, which allows to attach symmetry labels to its eigenvalues. Knowledge of the probabilities of plaquette occupation number configurations is useful for meticulous benchmarking of quantum gas microscope experiments. As the quantum state on the plaquette is exact and self-consistently embedded in an exact, correlated bath, the present approach connects to various cluster approximation techniques., Comment: 15 pages, 8 figures. Replacement is identical to the previously submitted version except that a serious formatting mistake has been corrected. Please refer to this version

Density-functional tight binding (DFTB) has become a popular form of approximate density-functional theory (DFT) based upon a minimal valence basis set and neglect of all but two center integrals. We report the results of our tests of a recent long-range correction (lc) for time-dependent (TD) lc-DFTB by carrying out TD-lc-DFTB fewest switches surface hopping (FSSH) calculations of energy and charge transfer times using the relatively new DFTBaby program. An advantage of this method is the ability to run enough trajectories to get meaningful ensemble averages. Our interest in the present work is less in determining exact energy and charge transfer rates than in understanding how the results of these calculations vary with the value of the range-separation parameter (Rlc = 1/{\mu}) for a model organic solar cell heterojunction consisting of a van der Waals complex P/F made up of single pentacene (P) molecule together with a single buckminsterfullerene (F) molecule. The default value of Rlc = 3.03 a0 is found to be much too small as neither energy nor charge transfer is observed until Rlc ~ 10 a0. Tests at a single geometry show that best agreement with high-quality ab-initio spectra is obtained in the limit of no lc (i.e., very large Rlc.) A plot of energy and charge transfer rates as a function of Rlc is provided which suggests that a value of Rlc ~ 15 a0 yields the typical literature charge transfer time of about 100 fs. However, energy and charge transfer times become as high as ~ 300 fs for Rlc ~ 25 a0. A closer examination of the charge transfer process P*/F to P+/F- shows that the initial electron transfer is accompanied by a partial delocalization of the P hole onto F which then relocalizes back onto P, consistent with a polaron-like picture in which the nuclei relax to stabilize the resultant redistribution of charges.

Exciton formation leads to J-bands in solid pentacene. Describing these exciton bands represents a challenge for both time-dependent (TD) density-functional theory (DFT) and for its semiempirical analogue, namely for TD density-functional tight binding (DFTB) for three reasons (i) solid pentacene and pentacene aggregates are bound only by van der Waals forces which are notoriously difficult to describe with DFT and DFTB, (ii) the proper description of the long-range coupling between molecules, needed to describe Davydov splitting, is not easy to include in TD-DFT with traditional functionals and in TD-DFTB, and (iii) mixing may occur between local and charge transfer excitons, which may, in turn, require special functionals. We assess how far TD-DFT and TD-DFTB have progressed towards a correct description of this type of exciton by including both a dispersion correction for the ground state and a range-separated hybrid functional for the excited state. Analytic results for parallel-stacked ethylene are derived which go beyond Kasha's exciton model in that we are able to make a clear distinction between charge transfer and energy transfer excitons. This is further confirmed when it is shown that range-separated hybrids have a markedly greater effect on charge-transfer excitons than on energy-transfer excitons in the case of parallel-stacked pentacenes. TD-DFT calculations with the CAM-B3LYP functional and TD-lc-DFT calculations lead to negligeable excitonic corrections for the herringbone crystal structure, possibly because of an overcorrection of charge-transfer effects. In this case, TD-DFT calculations with the B3LYP functional or TD-DFTB calculations parameterized to B3LYP give the best results for excitonic corrections for the herringbone crystal structure as judged from comparison with experimental spectra and with Bethe-Salpeter equation calculations from the literature.

We present a method for computing the full probability distribution function of quadratic observables for the Fermi-Hubbard model within the framework of determinantal quantum Monte Carlo. Especially, in cold atoms experiments with single site resolution, such full counting statistics can be obtained from repeated projective measurements. We demonstrate, that the full counting statistics can provide important information on the size of preformed pairs. Furthermore, we compute the full counting statistics of the staggered magnetization in the repulsive Hubbard model at half filling and find excellent agreement with recent experimental results. We show that current experiments are capable of probing the difference between the Hubbard model and the limiting Heisenberg model., Comment: 5+7 pages; 3+4 figures

A software package, called DFTBaby, is published, which provides the electronic structure needed for running non-adiabatic molecular dynamics simulations at the level of charge-consistent tight-binding DFT. A long-range correction is incorporated to avoid spurious charge transfer states. Excited state energies, their analytic gradients and scalar non-adiabatic couplings are computed using tight-binding TD-DFT. These quantities are fed into a molecular dynamics code, which integrates Newton's equations of motion for the nuclei together with the electronic Schr\"{o}dinger equation. Non-adiabatic effects are included by surface hopping. As an example, the program is applied to the optimization of excited states and non-adiabatic dynamics of polyfluorene. The python and Fortran source code is available at http://www.dftbaby.chemie.uni-wuerzburg.de/.

Direct dynamics methods using Gaussian wavepackets have to rely only on local properties, such as gradients and hessians at the center of the wavepacket, so as to be compatible with the usual quantum chemistry methods. Matrix elements of the potential energy surfaces between wavepackets therefore usually have to be approximated. It is shown, that if a modified form of valence bond theory is used instead of the usual MO-based theories, the matrix elements can be obtained exactly. This is so because the molecular Hamiltonian only contains the Coulomb potential, for which matrix elements between different basis functions (consisting of Gaussian nuclear and electronic orbitals) are all well-known. In valence bond theory the self-consistent field calculation can be avoided so that the matrix elements are analytical functions of the nuclear coordinates. A method for simulating non-adiabatic quantum dynamics is sketched, where coherent state trajectories are propagated "on the fly" on adiabatic potential energy surfaces without making approximations to the matrix elements responsible for the coupling between trajectories., Comment: early draft

An extension of the CCS-method [Chem. Phys. 2004, 304, p. 103-120] for simulating non-adiabatic dynamics with quantum effects of the nuclei is put forward. The time-dependent Schr\"{o}dinger equation for the motion of the nuclei is solved in a moving basis set. The basis set is guided by classical trajectories, which can hop stochastically between different electronic potential energy surfaces. The non-adiabatic transitions are modelled by a modified version of Tully's fewest switches algorithm. The trajectories consist of Gaussians in the phase space of the nuclei (coherent states) combined with amplitudes for an electronic wave function. The time-dependent matrix elements between different coherent states determine the amplitude of each trajectory in the total multistate wave function; the diagonal matrix elements determine the hopping probabilities and gradients. In this way, both intereference effects and non-adiabatic transitions can be described in a very compact fashion, leading to the exact solution if convergence with respect to the number of trajectories is achieved and the potential energy surfaces are known globally. The method is tested on a 2D model for a conical intersection [J. Chem. Phys., 1996, 104, p. 5517], where a nuclear wavepacket encircles the point of degeneracy between two potential energy surfaces and intereferes with itself. These intereference effects are absent in classical trajectory-based molecular dynamics but can be fully incorporated if trajectories are replaced by surface hopping coupled coherent states.

Motivated by recent experiments with a Penning ion trap quantum simulator, we perform numerically exact Stochastic Series Expansion quantum Monte Carlo simulations of long-range transverse-field Ising models on a triangular lattice for different decay powers $\alpha$ of the interactions. The phase boundary for the ferromagnet is obtained as a function of $\alpha$. For antiferromagnetic interactions, there is strong indication that the transverse field stabilizes a clock ordered phase with sublattice magnetization $(M,-\frac{M}{2}, -\frac{M}{2})$ with unsaturated $M < 1$ in a process known as "order by disorder" similar to the nearest neighbour antiferromagnet on the triangular lattice. Connecting the known limiting cases of nearest neighbour and infinite-range interactions, a semiquantitative phase diagram is obtained. Magnetization curves for the ferromagnet for experimentally relevant system sizes and with open boundary conditions are presented., Comment: 18 pages, 19 figures

We propose to create superposition states of over 100 Strontium atoms being in a ground state or metastable optical clock state, using the Kerr-type interaction due to Rydberg state dressing in an optical lattice. The two components of the superposition can differ by of order 300 eV in energy, allowing tests of energy decoherence models with greatly improved sensitivity. We take into account the effects of higher-order nonlinearities, spatial inhomogeneity of the interaction, decay from the Rydberg state, collective many-body decoherence, atomic motion, molecular formation and diminishing Rydberg level separation for increasing principal number., Comment: 10 pages, 5 figures

We present two improvements to the tight-binding approximation of time-dependent density functional theory (TD-DFTB): Firstly, we add an exact Hartree-Fock exchange term, which is switched on at large distances, to the ground state Hamiltonian and similarly to the coupling matrix that enters the linear response equations for the calculation excited electronic states. We show that the excitation energies of charge transfer states are improved relative to the standard approach without the long-range correction by testing the method on a set of molecules from the database in J. Chem. Phys. (2008),128,044118. that are known to exhibit problematic charge transfer states. The degree of spatial overlap between occupied and virtual orbitals indicates where TD-DFTB and lc-TD-DFTB can be expected to produce large errors. Secondly, we improve the calculation of oscillator strengths. The transition dipoles are obtained from Slater Koster files for the dipole matrix elements between valence orbitals. In particular excitations localized on a single atom, which appear dark when using Mulliken transition charges, in this way acquire a more realistic oscillator strength. These extensions pave the way for using long-range corrected TD-DFTB (lc-TD-DFTB) to describe the electronic structure of large chromophoric polymers, where uncorrected TD-DFTB fails to describe the high degree of conjugation and produces spurious low-lying charge transfer states., Comment: Keywords: DFT, TD-DFT, DFTB, TD-DFTB, tight-binding DFT, long-range correction, charge transfer

We present a general scheme for the calculation of the Renyi entropy of a subsystem in quantum many-body models that can be efficiently simulated via quantum Monte Carlo. When the simulation is performed at very low temperature, the above approach delivers the entanglement Renyi entropy of the subsystem, and it allows to explore the crossover to the thermal Renyi entropy as the temperature is increased. We implement this scheme explicitly within the Stochastic Series expansion as well as within path-integral Monte Carlo, and apply it to quantum spin and quantum rotor models. In the case of quantum spins, we show that relevant models in two dimensions with reduced symmetry (XX model or hardcore bosons, transverse-field Ising model at the quantum critical point) exhibit an area law for the scaling of the entanglement entropy., Comment: 5+1 pages, 4+1 figures