An infinite swapping approach to the rare-event sampling problem.

We describe a new approach to the rare-event Monte Carlo sampling problem. This technique utilizes a symmetrization strategy to create probability distributions that are more highly connected and, thus, more easily sampled than their original, potentially sparse counterparts. After discussing the formal outline of the approach and devising techniques for its practical implementation, we illustrate the utility of the technique with a series of numerical applications to Lennard-Jones clusters of varying complexity and rare-event character.

Band structure of SnTe studied by photoemission spectroscopy.

We present an angle-resolved photoemission spectroscopy study of the electronic structure of SnTe and compare the experimental results to ab initio band structure calculations as well as a simplified tight-binding model of the p bands. Our study reveals the conjectured complex Fermi surface structure near the L points showing topological changes in the bands from disconnected pockets, to open tubes, and then to cuboids as the binding energy increases, resolving lingering issues about the electronic structure. The chemical potential at the crystal surface is found to be 0.5 eV below the gap, corresponding to a carrier density of p=1.14 × 10(21) cm(-3) or 7.2 × 10(-2) holes per unit cell. At a temperature below the cubic-rhombohedral structural transition a small shift in spectral energy of the valance band is found, in agreement with model predictions.

Machine learning bandgaps of double perovskites.

The ability to make rapid and accurate predictions on bandgaps of double perovskites is of much practical interest for a range of applications. While quantum mechanical computations for high-fidelity bandgaps are enormously computation-time intensive and thus impractical in high throughput studies, informatics-based statistical learning approaches can be a promising alternative. Here we demonstrate a systematic feature-engineering approach and a robust learning framework for efficient and accurate predictions of electronic bandgaps of double perovskites. After evaluating a set of more than 1.2 million features, we identify lowest occupied Kohn-Sham levels and elemental electronegativities of the constituent atomic species as the most crucial and relevant predictors. The developed models are validated and tested using the best practices of data science and further analyzed to rationalize their prediction performance.

Classification of octet AB-type binary compounds using dynamical charges: A materials informatics perspective.

The role of dynamical (or Born effective) charges in classification of octet AB-type binary compounds between four-fold (zincblende/wurtzite crystal structures) and six-fold (rocksalt crystal structure) coordinated systems is discussed. We show that the difference in the dynamical charges of the fourfold and sixfold coordinated structures, in combination with Harrison's polarity, serves as an excellent feature to classify the coordination of 82 sp-bonded binary octet compounds. We use a support vector machine classifier to estimate the average classification accuracy and the associated variance in our model where a decision boundary is learned in a supervised manner. Finally, we compare the out-of-sample classification accuracy achieved by our feature pair with those reported previously.

Classification of ABO3 perovskite solids: a machine learning study.

We explored the use of machine learning methods for classifying whether a particular ABO3 chemistry forms a perovskite or non-perovskite structured solid. Starting with three sets of feature pairs (the tolerance and octahedral factors, the A and B ionic radii relative to the radius of O, and the bond valence distances between the A and B ions from the O atoms), we used machine learning to create a hyper-dimensional partial dependency structure plot using all three feature pairs or any two of them. Doing so increased the accuracy of our predictions by 2-3 percentage points over using any one pair. We also included the Mendeleev numbers of the A and B atoms to this set of feature pairs. Doing this and using the capabilities of our machine learning algorithm, the gradient tree boosting classifier, enabled us to generate a new type of structure plot that has the simplicity of one based on using just the Mendeleev numbers, but with the added advantages of having a higher accuracy and providing a measure of likelihood of the predicted structure.

Comparative Monte Carlo efficiency by Monte Carlo analysis.

We propose a modified power method for computing the subdominant eigenvalue λ{2} of a matrix or continuous operator. While useful both deterministically and stochastically, we focus on defining simple Monte Carlo methods for its application. The methods presented use random walkers of mixed signs to represent the subdominant eigenfunction. Accordingly, the methods must cancel these signs properly in order to sample this eigenfunction faithfully. We present a simple procedure to solve this sign problem and then test our Monte Carlo methods by computing λ{2} of various Markov chain transition matrices. As |λ{2}| of this matrix controls the rate at which Monte Carlo sampling relaxes to a stationary condition, its computation also enabled us to compare efficiencies of several Monte Carlo algorithms as applied to two quite different types of problems. We first computed λ{2} for several one- and two-dimensional Ising models, which have a discrete phase space, and compared the relative efficiencies of the Metropolis and heat-bath algorithms as functions of temperature and applied magnetic field. Next, we computed λ{2} for a model of an interacting gas trapped by a harmonic potential, which has a mutidimensional continuous phase space, and studied the efficiency of the Metropolis algorithm as a function of temperature and the maximum allowable step size Δ. Based on the λ{2} criterion, we found for the Ising models that small lattices appear to give an adequate picture of comparative efficiency and that the heat-bath algorithm is more efficient than the Metropolis algorithm only at low temperatures where both algorithms are inefficient. For the harmonic trap problem, we found that the traditional rule of thumb of adjusting Δ so that the Metropolis acceptance rate is around 50% is often suboptimal. In general, as a function of temperature or Δ , λ{2} for this model displayed trends defining optimal efficiency that the acceptance ratio does not. The cases studied also suggested that Monte Carlo simulations for a continuum model are likely more efficient than those for a discretized version of the model.

Monte Carlo determination of multiple extremal eigenpairs.

We present a Monte Carlo algorithm that allows the simultaneous determination of a few extremal eigenpairs of a very large matrix without the need to compute the inner product of two vectors or store all the components of any one vector. The algorithm, a Monte Carlo implementation of a deterministic one we recently benchmarked, is an extension of the power method. In the implementation presented, we used a basic Monte Carlo splitting and termination method called the comb, incorporated the weight cancellation method of Arnow et al, and exploited a sampling method, the sewing method, that does a large state space sampling as a succession of small state space samplings. We illustrate the effectiveness of the algorithm by its determination of the two largest eigenvalues of the transfer matrices for variously sized two-dimensional, zero-field Ising models. While very likely useful for other transfer-matrix problems, the algorithm is however quite general and should find application to a larger variety of problems requiring a few dominant eigenvalues of a matrix.

Strong coupling approach to actinide metals.

We present a strongly correlated approach to the electronic structure of actinide metals by deriving a low-energy Hamiltonian H[over] under the assumption that kinetic energy is small compared to Coulomb and spin-orbit interactions. The H[over]Pu for Pu metal is similar to the models used for Ce and other lanthanides but qualitatively different from the H[over] presented for the rest of the actinides. With H[over]Pu, we computed the photoemission spectrum and specific heat for alpha and delta-Pu and found good agreement with experiment.

Segmented band mechanism for itinerant ferromagnetism.

We introduce a novel mechanism for itinerant ferromagnetism, which is based on a simple two-band model, and, by using numerical and analytical methods, we show that the periodic Anderson model contains this mechanism. We propose that the mechanism, which does not assume an intra-atomic Hund's coupling, is present in both the iron group and some f electron compounds.

Intermediate coupling theory of electronic ferroelectricity.

We calculate the quantum phase diagram of an extended Falicov-Kimball model for one- and two-dimensional systems in the intermediate coupling regime. Even though some features of the phase diagram are obtained analytically, the main results are calculated with a constrained path Monte Carlo technique. We find that this regime is dominated by a Bose-Einstein condensation of excitons with a built-in electric polarization. The inclusion of a finite hybridization between the bands removes the condensate but reinforces the ferroelectricity.

Direct observation of itinerant magnetism in the 5f-electron system UTe.

Our electron photoemission experiments demonstrate that the magnetization of the ferromagnetic state of UTe is proportional to the binding energy of the hybridized band centered around 50 meV below EF. This proportionality is direct evidence that the ferromagnetism of UTe is itinerant; i.e., the 5f electrons are not fully localized close to the atomic core. This mechanism of itinerant ferromagnetism differs from the traditional picture for 5f-electron magnetism in an essential and a novel way. We propose a simple model for the observed proportionality between the temperature dependence of the magnetization and the binding energy of the hybridized band near EF. This model allows us to estimate the effective magnetic interaction and to identify signatures of itinerant ferromagnetism in other materials.