Publications

It is difficult to quantify structure–property relationships and to identify structural features of complex materials. The characterization of amorphous materials is especially challenging because their lack of long-range order makes it difficult to define structural metrics. In this work, we apply deep learning algorithms to accurately classify amorphous materials and characterize their structural features. Specifically, we show that convolutional neural networks and message passing neural networks can classify two-dimensional liquids and liquid-cooled glasses from molecular dynamics simulations with greater than 0.98 AUC, with no a priori assumptions about local particle relationships, even when the liquids and glasses are prepared at the same inherent structure energy. Furthermore, we demonstrate that message passing neural networks surpass convolutional neural networks in this context in both accuracy and interpretability. We extract a clear interpretation of how message passing neural networks evaluate liquid and glass structures by using a self-attention mechanism. Using this interpretation, we derive three novel structural metrics that accurately characterize glass formation. The methods presented here provide a procedure to identify important structural features in materials that could be missed by standard techniques and give unique insight into how these neural networks process data."

The role of planetary-scale zonally-asymmetric thermal forcing on large-scale atmospheric dynamics is crucial for understanding low-frequency phenomena in the atmosphere. Despite its paramount importance, good theoretical foundation for the understanding is still lacking. Here, we address this issue by providing a general framework for including planetary-scale thermal forcing in large-scale atmospheric dynamics studies. This is accomplished by identifying two distinct geostrophic motions of horizontal length scale Lin terms of the external Rossby deformation length scale LD: i) L ∼ ϵ0 LD and ii) L ∼ ϵ1/2 LD, whereϵ is the Rossby number. In addition, via multi-scale analysis, we show that the large-scale atmospheric dynamics can be described by mutual interaction between the two scales. The analysis results in planetary geostrophic equations with large-scale thermal forcing that provide the basic balanced states for processes such as the growth of synoptic waves. In the long-time limit, the continuous growth and decay of synoptic waves provide the convergence of horizontal heat and vorticity fluxes, which contributes to the energy flux balance in the planetary geostrophic scale with planetary-scale advection and thermal forcing.

The bilayer Hubbard model with electron-hole doping is an ideal platform to study excitonic orders due to suppressed recombination via spatial separation of electrons and holes. However, suffering from the sign problem, previous quantum Monte Carlo studies could not arrive at an unequivocal conclusion regarding the presence of phases with clear signatures of excitonic condensation in bilayer Hubbard models. Here, we develop a determinant quantum Monte Carlo (DQMC) algorithm for the bilayer Hubbard model that is sign-problem-free for equal and opposite doping in the two layers, and study excitonic order and charge and spin density modulations as a function of chemical potential difference between the two layers, on-site Coulomb repulsion, and inter-layer interaction. In the intermediate coupling regime and in proximity to the SU(4)-symmetric point, we find a biexcitonic condensate phase at finite electron-hole doping, as well as a competing (π,π) charge density wave (CDW) state. We extract the Berezinskii-Kosterlitz-Thouless (BKT) transition temperature from superfluid density and a finite size scaling analysis of the correlation functions, and explain our results in terms of an effective biexcitonic hardcore boson model.

The brain takes uncertainty intrinsic to our world into account. For example, associating spatial locations with rewards requires to predict not only expected reward at new spatial locations but also its uncertainty to avoid catastrophic events and forage safely. A powerful and flexible framework for nonlinear regression that takes uncertainty into account in a principled Bayesian manner is Gaussian process (GP) regression. Here I propose that the brain implements GP regression and present neural networks (NNs) for it. First layer neurons, e.g. hippocampal place cells, have tuning curves that correspond to evaluations of the GP kernel. Output neurons explicitly and distinctively encode predictive mean and variance, as observed in orbitofrontal cortex (OFC) for the case of reward prediction. Because the weights of a NN implementing exact GP regression do not arise with biological plasticity rules, I present approximations to obtain local (anti-)Hebbian synaptic learning rules. The resulting neuronal network approximates the full GP well compared to popular sparse GP approximations and achieves comparable predictive performance.

We theoretically investigate the effects of the lattice geometry on the nonequilibrium dynamics of photo-excited carriers in a half-filled two-dimensional Hubbard model. Using a nonequilibrium generalization of the dynamical cluster approximation, we compare the relaxation dynamics in lattices which interpolate between the triangular lattice and square lattice configuration and thus reveal the role of the geometric frustration in these strongly correlated nonequilibrium systems. In particular, we show that the cooling effect resulting from the disordering of the spin background is less effective in the triangular case because of the frustration. This manifests itself in a longer relaxation time of the photo-doped population, as measured by the time-resolved photo-emission signal, and a higher effective temperature of the photo-doped carriers in the non-thermal steady state after the intra-Hubbard-band thermalization.

We perform extensive auxiliary-field quantum Monte Carlo (AFQMC) calculations for the three-band Hubbard (Emery) model in order to study the ground-state properties of Copper-Oxygen planes in the cuprates. Employing cutting-edge AFQMC techniques with a self-consistent gauge constraint in auxiliary-field space to control the sign problem, we reach supercells containing around 500 atoms to capture collective modes in the charge and spin orders and characterize the behavior in the thermodynamic limit. The self-consistency scheme interfacing with generalized Hartree-Fock calculations allows high accuracy in AFQMC to resolve small energy scales, which is crucial for determining the complex candidate orders in such a system. We present detailed information on the charge order, spin order, momentum distribution, and localization properties as a function of charge-transfer energy for the the under-doped regime. In contrast with the stripe and spiral orders under hole-doping, we find that the corresponding 1/8 electron-doped system exhibits purely antiferromagnetic order in the three-band model, consistent with the asymmetry between electron and hole-doping in the phase diagram of cuprates.

In this article, we provide a pedagogical review of the theory of topological quantum chemistry and topological crystalline insulators. We begin with an overview of the properties of crystal symmetry groups in position and momentum space. Next, we introduce the concept of a band representation, which quantifies the symmetry of topologically trivial band structures. By combining band representations with symmetry constraints on the connectivity of bands in momentum space, we show how topologically nontrivial bands can be catalogued and classified. We present several examples of new topological phases discovered using this paradigm, and conclude with an outlook towards future developments.

We present a general formalism that allows for the computation of large-order renormalized expansions in the spacetime representation, effectively doubling the numerically attainable perturbation order of renormalized Feynman diagrams. We show that this formulation compares advantageously to the currently standard techniques due to its high efficiency, simplicity, and broad range of applicability. Our formalism permits to easily complement perturbation theory with non-perturbative information, which we illustrate by implementing expansions renormalized by the addition of a gap or the inclusion of Dynamical Mean-Field Theory. As a result, we present numerically-exact results for the square-lattice Fermi-Hubbard model in the low temperature non-Fermi-liquid regime and show the momentum-dependent suppression of fermionic excitations in the antinodal region.

A method to calculate the one-body Green's function for ground states of correlated electron materials is formulated by extending the variational Monte Carlo method. We benchmark against the exact diagonalization (ED) for the one- and two-dimensional Hubbard models of 16 site lattices, which proves high accuracy of the method. The application of the method to larger-sized Hubbard model on the square lattice correctly reproduces the Mott insulating behavior at half filling and gap structures of d-wave superconducting state of the hole doped Hubbard model in the ground state optimized by enforcing the charge uniformity, evidencing a wide applicability to strongly correlated electron systems. From the obtained d-wave superconducting gap of the charge uniform state, we find that the gap amplitude at the antinodal point is several times larger than the experimental value, when we employ a realistic parameter as a model of the cuprate superconductors. The effective attractive interaction of carriers in the d-wave superconducting state inferred for an optimized state of the Hubbard model is as large as the order of the nearest-neighbor transfer, which is far beyond the former expectation in the cuprates. We discuss the nature of the superconducting state of the Hubbard model in terms of the overestimate of the gap and the attractive interaction in comparison to the cuprates.

Predicting the properties of a quantum-mechanical system of many interacting particles is a major goal of modern science and an outstanding challenge. We consider a compact and versatile model which captures the essential features of a broad class of systems made of particles obeying Bose–Einstein statistics and which allows one to systematically dial up the effect of quantum entanglement in the presence of particle interaction by tuning a single parameter. We are able to obtain exact numerical results for the phase diagrams of these systems. Possible directions for experimental realization of the predictions are discussed.We present a comprehensive theoretical study of the phase diagram of a system of many Bose particles interacting with a two-body central potential of the so-called Lennard-Jones form. First-principles path-integral computations are carried out, providing essentially exact numerical results on the thermodynamic properties. The theoretical model used here provides a realistic and remarkably general framework for describing simple Bose systems ranging from crystals to normal fluids to superfluids and gases. The interplay between particle interactions on the one hand and quantum indistinguishability and delocalization on the other hand is characterized by a single quantumness parameter, which can be tuned to engineer and explore different regimes. Taking advantage of the rare combination of the versatility of the many-body Hamiltonian and the possibility for exact computations, we systematically investigate the phases of the systems as a function of pressure (P) and temperature (T), as well as the quantumness parameter. We show how the topology of the phase diagram evolves from the known case of 4He, as the system is made more (and less) quantum, and compare our predictions with available results from mean-field theory. Possible realization and observation of the phases and physical regimes predicted here are discussed in various experimental systems, including hypothetical muonic matter.There are no data underlying this work.