# J. E. Gubernatis's research while affiliated with Santa Fe College and other places

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## Publications (197)

In this final chapter, we present three, somewhat independent, short essays on topics that provide an important perspective on the nature of machine learning, propose a potential future machine learning opportunity for materials design and discovery, and make some comments about the use of machine learning in experimental material science. In the f...

From a point of view that is both complementary and supplementary, this chapter revisits some of the uses and opportunities for materials design and discovery just discussed in Section 2.2.3. The previous subsection’s focus was mainly about macroscopic-scale feature generation and selection and illustrated the benefit that attention on both topics...

The title of one of the seminal papers in the field of multi-fidelity learning and optimization, “Predicting the Output from a Complex Computer Code when Fast Approximations are Available,” gives a good hint at what multi-fidelity optimization and learning is. It is about building an accurate surrogate model for a complex problem based on the parti...

In this chapter, we discuss perhaps the most important component of machine learning model building—the one that converts a molecular or material system into a numerical representation. To build the models, we use a machine learning algorithm. What we will be discussing is defining the random variables on which the models depend. The chosen statist...

In contrast to the combinatorial approaches using high throughput calculations that generate large data sets on ideal systems at T = 0 and P = 0 discussed in Chapter 3 and elsewhere in this book, real materials problems typically involve several components, are often solid solutions, and contain defects at T ≠ 0 and P ≠ 0. For crystals however, ele...

Real engineering problems are generally multi-objective where one or more properties must be simultaneously optimized. In a multi-objective optimization problem, we rarely have a unique solution that satisfies all the constraints associated with all the objectives. Instead, we settle for “trade-offs” and find acceptable solutions that balance the t...

We provide a brief discussion of “What is machine learning?” and then give a number of examples of how these methods have recently aided the design and discovery of new materials, such as new shape memory alloys, with enhanced targeted properties, such as lower hysteresis. These examples illustrate how discoveries can be made from large databases,...

In materials informatics, features (or descriptors) that capture trends in the structure, chemistry and/or bonding for a given chemical composition are crucial. Here, we explore their role in the accelerated search for new materials using machine learning adaptive design. We focus on a specific class of materials referred to as apatites [A\(_{10}\)...

We apply machine learning (ML) methods to a database of 390 experimentally reported ABO3 compounds to construct two statistical models that predict possible new perovskite materials and possible new cubic perovskites. The first ML model classified the 390 compounds into 254 perovskites and 136 that are not perovskites with a 90% average cross-valid...

Guiding experiments to find materials with targeted properties is a crucial aspect of materials discovery and design, and typically multiple properties, which often compete, are involved. In the case of two properties, new compounds are sought that will provide improvement to existing data points lying on the Pareto front (PF) in as few experiments...

Abstract We present a multi-fidelity co-kriging statistical learning framework that combines variable-fidelity quantum mechanical calculations of bandgaps to generate a machine-learned model that enables low-cost accurate predictions of the bandgaps at the highest fidelity level. In addition, the adopted Gaussian process regression formulation allo...

For three datasets, all dealing with materials with ABO\(_3\) chemistries, the two data visualizations algorithms
of Tsafrir et al. [Bioinformatics 21, 2301 (2005)] were studied and applied. These algorithms permute the distance matrix
associated with the data in a way to unveil structure in one case by keeping large-distanced information afar or i...

We present two Monte Carlo algorithms to find the Pareto front of the chemical space of a class of dielectric polymers that is most interesting with respect to optimizing both the bandgap and dielectric constant. Starting with a dataset generated from density functional theory calculations, we used machine learning to construct surrogate models for...

We review how classification and regression methods have been used on materials problems and outline a design loop that serves as a basis for adaptively finding materials with targeted properties.

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 combi...

By using the constrained-phase quantum Monte Carlo method, we performed a
systematic study of the pairing correlations in the ground state of the doped
Kane-Mele-Hubbard model. We find that pairing correlations with $d+id$ symmetry
dominate close to half filling, while pairing correlations with $p+ip$ symmetry
dominate as hole doping moves the syst...

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...

Machine learning methods are being increasingly used in condensed matter physics and materials science to classify crystals structures and predict material properties. However, the reliability of these methods for a given problem, especially when large data sets are unavailable, has not been well studied. By addressing the tasks of classifying crys...

We investigate the effect of spin-orbit coupling on the behavior of magnetic
impurity at the edge of a zigzag graphene ribbon by means of quantum Monte
Carlo simulations. A peculiar interplay of Kane-Mele type spin-orbit and
impurity-host coupling is found to affect local properties such as the impurity
magnetic moment and spectral densities. The s...

We calculate the quantum phase diagram of an extended Falicov-Kimball model in the intermediate coupling regime using a constrained path quantum Monte Carlo technique. The mixed-valence regime is dominated by a Bose-Einstein condensation of excitons with a built-in electric polarization.

With quantum Monte Carlo methods, we investigate the consequences of placing
a magnetic adatom adjacent to a vacancy in a graphene sheet. We find that
instead of the adatom properties depending on the energy of the adatom orbital,
as in a single impurity problem, they develop a dependence on the energy of the
split localized state associated with t...

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...

We used a quantum Monte Carlo method to study the magnetic impurity adatoms
on graphene. We found that by tuning the chemical potential we could switch the
values of the impurity's local magnet moment between relatively large and small
values. Our computations of the impurity's spectral density found its behavior
to differ significantly from that o...

We investigate the Periodic Anderson model in the regime of itinerant ferromagnetism. We compare Quantum Monte Carlo (QMC)
results with results obtained using the Gutzwiller approximation (GA). As expected, the energy of the paramagnetic state is
overestimated by the GA in comparison with QMC results; however, the partially saturated ferromagnetic...

Within the framework of nonequilibrium Green's functions, we investigate the
thermoelectric transport in a single molecular junction with electron-phonon
and electron-electron interactions. By transforming into a displaced phonon
basis, we are able to deal with these interactions non-perturbatively. Then, by
invoking the weak tunneling limit, we ar...

We report resonant ultrasound spectroscopy (RUS), dilatometry/magnetostriction, magnetotransport, magnetization, specific heat, and $^{119}$Sn M\"ossbauer spectroscopy measurements on SnTe and Sn$_{0.995}$Cr$_{0.005}$Te. Hall measurements at $T=77$ K indicate that our Bridgman-grown single crystals have a $p$-type carrier concentration of $3.4 \tim...

We propose a modified power method for computing the subdominant eigenvalue $\lambda_2$ of a matrix or continuous operator. Here we focus on defining simple Monte Carlo methods for its application. The methods presented use random walkers of mixed signs to represent the subdominant eigenfuction. Accordingly, the methods must cancel these signs prop...

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...

Recently, we proposed a modified power iteration method that simultaneously determines the dominant and subdominant eigenvalues and eigenfunctions of a matrix or a continuous operator. One advantage of this method is the convergence rate to the dominant eigenfunction being |k3|/k1 instead of |k2|/k1, a potentially significant acceleration. One chal...

We observe ferromagnetic ordering at 298 K by magnetic susceptibility measurements. In addition we observe a structural transition at 98 K that has been attributed to ferroelectricity. Transmission electron microscopy at 300 K shows a modulated cubic structure thereby challenging the heretofore accepted B1 rocksalt structure. Ramifications of these...

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 t...

We describe a method for treating the sparse or rare-event sampling problem. Our approach is based on the introduction of a family of modified importance functions, functions that are related to but easier to sample than the original statistical distribution. We quantify the performance of the approach for a series of example problems using an asym...

Nuclear criticality calculations with Monte Carlo codes are normally done using a power iteration method to obtain the dominant eigenfunction and eigenvalue, In the last few years it has been shown that the power iteration method can be modified to obtain the first two eigenfunctions. This modified power iteration method directly subtracts out the...

We present a procedure that in many cases enables the Monte Carlo sampling of states of a large system from the sampling of states of a smaller system. We illustrate this procedure, which we call the sewing algorithm, for sampling states from the transfer matrix of the two-dimensional Ising model. Comment: 9 pages, no figures

We present a new Monte Carlo algorithm that allows the simultaneous determination of a few extremal eigenpairs of a very large matrix. It extends the power method and uses a new sampling method, the sewing method, that does a large state space sampling as a succession of samplings from a smaller state space. We illustrate the new algorithm by its d...

We report the production and benchmarking of several refinements of the power method that enable the computation of multiple extremal eigenpairs of very large matrices. In these refinements we used an observation by Booth that has made possible the calculation of up to the 10$^{th}$ eigenpair for simple test problems simulating the transport of neu...

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 fro...

We present a pedagogical discussions of the dynamical mean field (DMFA) and dynamical cluster (DCA) approximations and associated Monte Carlo and entropy‐based methods of Bayesian
data analysis. The DMFA and DCA methods are developed as coarse‐graining approximations and the relationship between the cluster and lattice problems are detailed. The H...

Relative to single-band models, multiband models of strongly interacting electron systems are of growing interest because of their wider range of novel phenomena and their closer match to the electronic structure of real materials. In this brief review we discuss the physics of three multiband models (the three-band Hubbard, the periodic Anderson,...

Described are the details for performing Monte Carlo simulations on systems of fermions at finite temperatures by use of a
technique called the Determinant Method. This method is based on a functional integral formulation of the fermion problem
[Blankenbecler et al., Phys. Rev. D 24, 2278 (1981)] in which the quartic fermion-fermion interactions th...

The periodic Anderson model is believed as a candidate of the minimal lattice models for itinerant ferromagnetism. Several numerical methods, including exactly diagonalization, constrained-path Monte Carlo method and mean field method, are employed to investigate the magnetic properties of the model in one dimension and two dimensions. By changing...

We study the strong coupling limit of a two-band Hubbard Hamiltonian that also includes an inter-orbital on-site repulsive interaction $U_{ab}$. When the two bands have opposite parity and are quarter filled, we prove that the ground state is simultaneously ferromagnetic and ferroelectric for infinite intra-orbital Coulomb interactions $U_{aa}$ and...

A recent paper by Matuttis and Ito questions the numerical accuracy of a widely-used fermion Monte Carlo algorithm. They also claim that the increase in the d-wave pairfield susceptibility chid(T) of a doped 4×4 Hubbard model at low temperature, previously found using this algorithm, is an artifact due to numerical errors. Here, we provide tests wh...

The 1953 publication, “Equation of State Calculations by Very Fast Computing Machines” by N. Metropolis, A. W. Rosenbluth and M. N. Rosenbluth, and M. Teller and E. Teller
[J. Chem. Phys. 21, 1087 (1953)
] marked the beginning of the use of the Monte Carlo method for solving problems in the physical sciences. The method described in this publicatio...

Magnetic properties of 5f systems as seen by characteristic features in the valence band photoemission are discussed, with particular focus on ferromagnetic uranium compounds. As shown by the authors, electron photoemission experiments demonstrate that the magnetization of the ferromagnetic state of UTe is proportional to the binding energy of the...

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 ato...

We briefly review the results of recent work establishing a new mechanism for itinerant ferromagnetism in the periodic Anderson model. The novel mechanism, called the segmented band mechanism, whose energy scale is up to two orders of magnitude larger than the RKKY mechanism, is determined by a competition between two energy scales set by certain b...

Using the exact diagonalization and constrained path Monte Carlo methods, we investigate the effects of impurity f-band dispersion on the magnetic properties of Periodic Anderson lattice model in one and two dimensions (square lattice). The model is defined by the Hamiltonian: H=t(di,j,sigma)Sigma(d(isigma)(dagger)d(jsigma)+H.c.)+t(fi,j,sigma)Sigma...

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...

In a previous article [J. Phys. Chem. 21: 1087 (1953)] a prescription was given for moving from point to point in the configuration space of a system in such a way that averaging over many moves is equivalent to a canonical averaging over configuration space. The prescription is suitable for electronic machine calculations and provides the basis fo...

I present some early history of Los Alamos, modern computing, and the
Monte Carlo method to describe the likely context in which the
Metropolis algorithm was developed and to support the special creativity
of the development. I also note the scant immediate use of the algorithm
over the 10 to 15 years after its development and speculate why. This
s...

We determine exactly the ground state of the one-dimensional periodic Anderson model (PAM) in the strong hybridization regime. In this regime, the low energy sector of the PAM maps into an effective Hamiltonian that has a ferromagnetic ground state for any electron density between half and three quarters filling. This rigorous result proves the exi...

If a large Quantum Computer (QC) existed today, what type of physical problems could we efficiently simulate on it that we could not simulate on a classical Turing machine? In this paper we argue that a QC could solve some relevant physical "questions" more efficiently. The existence of one-to-one mappings between different algebras of observables...

As a result of the capabilities of quantum information, the science of quantum information processing is now a prospering, interdisciplinary field focused on better understanding the possibilities and limitations of the underlying theory, on developing new applications of quantum information and on physically realizing controllable quantum devices....

We introduce a novel mechanism for itinerant ferromagnetism, based on a simple two-band model. The model includes an uncorrelated and dispersive band hybridized with a second band which is narrow and correlated. The simplest Hamiltonian containing these ingredients is the Periodic Anderson Model (PAM). Using quantum Monte Carlo and analytical metho...

We present a new mechanism for itinerant ferromagnetism in mixed valent materials, and using the constrained path quantum Monte Carlovmethod, we demonstrate its presence in the periodic Anderson model. The mechanism relies on the hybridization between two band segmenting the Brillouin zone into regions dominated by electron states that are localize...

We review our bivariate multicanonical Monte Carlo simulation of the ±J spin glass in three dimensions as well as recent developments on the controversy between the droplet picture and the mean-field picture of the spin-glass phase.

We present an algebraic framework for identifying the order parameter and the possible phases of quantum systems that is based on identifying the local dimension $N$ of the quantum operators and using the SU(N) group representing the generators of generalized spin-particle mappings. We illustrate this for $N$=3 by presenting for any spatial dimensi...

The real-time probabilistic simulation of quantum systems in classical computers is known to be limited by the so-called dynamical sign problem, a problem leading to exponential complexity. In 1981 Richard Feynman raised some provocative questions in connection to the “exact imitation” of such systems using a special device named a “quantum compute...

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 e...

The goal of physics simulation using controllable quantum systems (“physics imitation”) is to exploit quantum laws to advantage, and thus accomplish efficient simulation of physical phenomena. In this Note, we discuss the fundamental concepts behind this paradigm of information processing, such as the connection between models of computation and ph...

We investigate the simulation of fermionic systems on a quantum computer. We show in detail how quantum computers avoid the dynamical sign problem present in classical simulations of these systems, therefore reducing a problem believed to be of exponential complexity into one of polynomial complexity. The key to our demonstration is the spin-partic...

Using the recently developed constrained-path Monte Carlo method, we have completed a series of ground state computations of pairing correlation functions in two-dimensional extended one-band and three-band Hubbard models. We found that dx2−y2-wave pairing correlations dominated s-wave correlations but that these correlations were suppressed by inc...

To clarify the effects of next-nearest-neighbor electron hopping t′ on the spin, charge, and pairing correlations, we studied the two-dimensional t-t′-U Hubbard model using the constrained-path Monte Carlo technique. We found that a negative t′ suppresses the spin fluctuations near the Brillouin zone point M=(π,π) and the charge fluctuations near t...

Physical systems, characterized by an ensemble of interacting elementary constituents, can be represented and studied by different algebras of observables or operators. For example, a fully polarized electronic system can be investigated by means of the algebra generated by the usual fermionic creation and annihilation operators, or by using the al...

We investigate the simulation of fermionic systems on a quantum computer. We show in detail how quantum computers avoid the dynamical sign problem present in classical simulations of these systems, therefore reducing a problem believed to be of exponential complexity into one of polynomial complexity. The key to our demonstration is the spin-partic...

Using the Constrained-Path Monte Carlo method, we performed a series of zero temperature quantum Monte Carlo simulations of the two-dimensional periodic Anderson model. We found three regimes of partially saturated ferromagnetic behavior and in each regime we able to identify the physical mechanism causing this behavior. In the mixed-valence regime...

We introduce a novel mechanism for the unusual itinerant ferromagnetism found in mixed valence systems like Ce(Rh$_{1-x}$Ru$_x$)$_3$B$_2$, La$_x$Ce$_{1-x}$Rh$_3$B$_2$, US, USe, and UTe. With it we can provide an explanation for the long-unexplained large value of $T_c$ ($\sim$ 100$^\circ$K) value and the maximum in the magnetization below $T_c$ fou...

The hole binding energy and pairing correlations are calculated in the three-band Hubbard model by using the constrained-path Monte Carlo (CPMC) method. In the physically relevant region, we investigated effects of CuO Coulomb repulsion Vpd on these two properties. Simulations were performed on lattices of 2×2, 4×2 and 6×4 unit cells. For the 2×2...

Using the Constrained Path Monte Carlo (CPMC) method, we simulated the two-dimensional, three-band Hubbard model to study pairing, charge, and spin correlations as a function of electron and hole doping and the Coulomb repulsion $V_{pd}$ between charges on neighboring Cu and O lattice sites. As a function of distance, both the $d_{x^2 - y^2}$-wave...

Using the constrained-path Monte Carlo method, we studied the magnetic properties of the two-dimensional periodic Anderson model for electron fillings between 1/4 and 1/2. We also derived two effective low energy theories to assist in interpreting the numerical results. For 1/4 filling we found that the system can be a Mott or a charge transfer ins...

We report the results of zero-temperature quantum Monte Carlo simulations and zero-temperature mean-field calculations of the attractive Hubbard model on chains, ladders, and square lattices. We investigated the predictability of the BCS approximation, the dimensional crossover of the pairing correlation function from one to two dimensions as a fun...

The search for a superconducting state in the two-dimensional one-band Hubbard model (HM) has been intense in the last few years. Monte Carlo methods, haunted by the infamous fermion sign problem, have been unable to study large enough systems and low enough temperatures. The Constrained Path Monte Carlo method (CPMC) evades the sign problem by int...

A bivariate multicanonical Monte Carlo simulation of the three-dimensional ±J Ising spin glass is described. The correlation time of the Monte Carlo dynamics is approximately proportional to the system
size, which is a great improvement over previous spin-glass simulations. The order-parameter distribution function P(q) at T=0.3 exhibits a feature...

DOI:https://doi.org/10.1103/PhysRevLett.84.2550

Using the constrained-path Monte Carlo (CPMC) method, we have studied the one-dimensional d-p model for the cases with finite Coulomb repulsion on d sites, and mainly examined the effects of transfer energy t_pp between the nearest-neighbor p sites on pairing correlations with different symmetry. Of these pairing correlations, we observed that only...

We give a brief discussion of the recently developed Constrained-Path Monte Carlo Method. This method is a quantum Monte Carlo technique that eliminates the fermion sign problem plaguing simulations of systems of interacting electrons. The elimination is accomplished by trading an exact procedure for an approximate one that has been demonstrated to...

The low-temperature behavior of spin glasses in three dimensions has been the subject of a long-standing, unresolved controversy between the mean-field picture, (which maintains the existence of an infinite number of free-energy minima due to replica symmetry breaking) and the droplet pincture (which claims that only two minima exist). In hope of r...

We report several important observations that underscore the distinctions between the constrained-path Monte Carlo method and the continuum and lattice versions of the fixed-node method. The main distinctions stem from the differences in the state space in which the random walk occurs and in the manner in which the random walkers are constrained. O...

We present a formulation of the Constrained Path Monte Carlo (CPMC) method for fermions that uses trial wave-functions that include many-body effects. This new formulation allows us to implement a whole family of generalized mean-field states as constraints. As an example, we calculated superconducting pairing correlation functions for the two-dime...

We studied the effects of hole doping on spin correlations in the periodic Anderson model, mainly at the full and three-quarters-full lower bands cases. In the full lower band case, strong anti-ferromagnetic correlations develop when the on-site repulsive interaction strength $U$ becomes comparable to the quasi-particle band width. In the three-qua...

We revisit the two-dimensional Hubbard model using the Constrained Path Monte Carlo method by generalizing a previous study by Zhang et al( S. Zhang, J. Carlson and J. E. Gubernatis, Phys. Rev. Lett. 78), 4485 (1997). in which simple free-electron or unrestricted Hartree-Fock wave-functions were used as constraints. In that case, the superconductin...

Using both the density-matrix renormalization group method and the constrained-path quantum Monte Carlo method, we have studied the ground-state energies and the spin and hole densities of a $12 \times 3$ Hubbard model with open boundary conditions and 6 holes doped away from half-filling. Results obtained with these two methods agree well in the s...