Publications

The auxiliary-field quantum Monte Carlo (AFQMC) method is a general numerical method for correlated many-electron systems, which is being increasingly applied in lattice models, atoms, molecules, and solids. Here we introduce the theory and algorithm of the method specialized for real materials, and present several recent developments. We give a systematic exposition of the key steps of AFQMC, closely tracking the framework of a modern software library we are developing. The building of a Monte Carlo Hamiltonian, projecting to the ground state, sampling two-body operators, phaseless approximation, and measuring ground state properties are discussed in details. An advanced implementation for multi-determinant trial wave functions is described which dramatically speeds up the algorithm and reduces the memory cost. We propose a self-consistent constraint for real materials, and discuss two flavors for its realization, either by coupling the AFQMC calculation to an effective independent-electron calculation, or via the natural orbitals of the computed one-body density matrix.

The emerging field of twistronics, which harnesses the twist angle between two-dimensional materials, represents a promising route for the design of quantum materials, as the twist-angle-induced superlattices offer means to control topology and strong correlations. At the small twist limit, and particularly under strain, as atomic relaxation prevails, the emergent moiré superlattice encodes elusive insights into the local interlayer interaction. Here we introduce moiré metrology as a combined experiment-theory framework to probe the stacking energy landscape of bilayer structures at the 0.1 meV/atom scale, outperforming the gold-standard of quantum chemistry. Through studying the shapes of moiré domains with numerous nano-imaging techniques, and correlating with multi-scale modelling, we assess and refine first-principle models for the interlayer interaction. We document the prowess of moiré metrology for three representative twisted systems: bilayer graphene, double bilayer graphene and H-stacked MoSe

Comprehensive and spatially mapped molecular atlases of organs at a cellular level are a critical resource to gain insights into pathogenic mechanisms and personalized therapies for diseases. The Kidney Precision Medicine Project (KPMP) is an endeavor to generate 3-dimensional (3D) molecular atlases of healthy and diseased kidney biopsies using multiple state-of-the-art OMICS and imaging technologies across several institutions. Obtaining rigorous and reproducible results from disparate methods and at different sites to interrogate biomolecules at a single cell level or in 3D space is a significant challenge that can be a futile exercise if not well controlled. We describe a "follow the tissue" pipeline for generating a reliable and authentic single cell/region 3D molecular atlas of human adult kidney. Our approach emphasizes quality assurance, quality control, validation and harmonization across different OMICS and imaging technologies from sample procurement, processing, storage, shipping to data generation, analysis and sharing. We established benchmarks for quality control, rigor, reproducibility and feasibility across multiple technologies through a pilot experiment using common source tissue that was processed and analyzed at different institutions and different technologies. A peer review system was established to critically review quality control measures and the reproducibility of data generated by each technology before being approved to interrogate clinical biopsy specimens. The process established economizes the use of valuable biopsy tissue for multi-OMICS and imaging analysis with stringent quality control to ensure rigor and reproducibility of results and serves as a model for precision medicine projects across laboratories, institutions and consortia.

We present a fast algorithm for computing the diffracted field from arbitrary binary (sharp-edged) planar apertures and occulters in the scalar Fresnel approximation, for up to moderately high Fresnel numbers ($\lesssim 10^3$). It uses a high-order areal quadrature over the aperture, then exploits a single 2D nonuniform fast Fourier transform (NUFFT) to evaluate rapidly at target points (of order $10^7$ such points per second, independent of aperture complexity). It thus combines the high accuracy of edge integral methods with the high speed of Fourier methods. Its cost is ${\mathcal O}(n^2 \log n)$, where $n$ is the linear resolution required in source and target planes, to be compared with ${\mathcal O}(n^3)$ for edge integral methods. In tests with several aperture shapes, this translates to between 2 and 5 orders of magnitude acceleration. In starshade modeling for exoplanet astronomy, we find that it is roughly $10^4 \times$ faster than the state of the art in accurately computing the set of telescope pupil wavefronts. We provide a documented, tested MATLAB/Octave implementation.
An appendix shows the mathematical equivalence of the boundary diffraction wave, angular integration, and line integral formulae, then analyzes a new non-singular reformulation that eliminates their common difficulties near the geometric shadow edge. This supplies a robust edge integral reference against which to validate the main proposal.

The early Drosophila embryo provides unique experimental advantages for addressing fundamental questions of gene regulation at multiple levels of organization, from individual gene loci to the whole genome. Using Drosophila embryos undergoing the first wave of genome activation, we detected discrete “speckles” of RNA Polymerase II (Pol II), and showed that they overlap with transcribing loci. We characterized the spatial distribution of Pol II speckles and quantified how this distribution changes in the absence of the primary driver of Drosophila genome activation, the pioneer factor Zelda. Although the number and size of Pol II speckles were reduced, indicating that Zelda promotes Pol II speckle formation, we observed a uniform distribution of distances between active genes in the nuclei of both wildtype and zelda mutant embryos. This suggests that the topologically associated domains identified by Hi-C studies do little to spatially constrain groups of transcribed genes at this time. We provide evidence that linear genomic distance between transcribed genes is the primary determinant of measured physical distance between the active loci. Furthermore, we show active genes can have distinct Pol II pools even if the active loci are in close proximity. In contrast to the emerging model whereby active genes are clustered to facilitate co-regulation and sharing of transcriptional resources, our data support an “individualist” model of gene control at early genome activation in Drosophila. This model is in contrast to a “collectivist” model where active genes are spatially clustered and share transcriptional resources, motivating rigorous tests of both models in other experimental systems.

Quantum phase estimation is at the heart of most quantum algorithms with exponential speedup. In this letter we demonstrate how to utilize it to compute the dynamical response functions of many-body quantum systems. Specifically, we design a circuit that acts as an efficient quantum generative model, providing samples out of the spectral function of high rank observables in polynomial time. This includes many experimentally relevant spectra such as the dynamic structure factor, the optical conductivity or the NMR spectrum. Experimental realization of the algorithm, apart from logarithmic overhead, requires doubling the number of qubits as compared to a simple analog simulator.

Many-body theories such as dynamical mean field theory (DMFT) have enabled the description of the electron exchange-correlation interactions that are missing in current density functional theory (DFT) calculations. However, there has been relatively little focus on the wavefunctions from these theories. We present the methodology of the newly developed Elk-TRIQS interface and how to calculate the DFT with DMFT (DFT+DMFT) wavefunctions, which can be used to calculate DFT+DMFT wavefunction dependent quantities. We illustrate this by calculating the electron localized function (ELF) in monolayer SrVO

The three-dimensional structure of human chromosomes is tied to gene regulation and replication timing, but there is still a lack of consensus on the computational and biological definitions for chromosomal substructures such as topologically associating domains (TADs). TADs are described and identified by various computational properties leading to different TAD sets with varying compatibility with biological properties such as boundary occupancy of structural proteins. We unify many of these computational and biological targets into one algorithmic framework that jointly maximizes several computational TAD definitions and optimizes TAD selection for a quantifiable biological property. Using this framework, we explore the variability of TAD sets optimized for six different desirable properties of TAD sets: high occupancy of CTCF, RAD21, and H3K36me3 at boundaries, reproducibility between replicates, high intra- vs inter-TAD difference in contact frequencies, and many CTCF binding sites at boundaries. The compatibility of these biological targets varies by cell type, and our results suggest that these properties are better reflected as subpopulations or families of TADs rather than a singular TAD set fitting all TAD definitions and properties. We explore the properties that produce similar TAD sets (reproducibility and inter- vs intra-TAD difference, for example) and those that lead to very different TADs (such as CTCF binding sites and inter- vs intra-TAD contact frequency difference).

Living matter moves, deforms, and organizes itself. In cells this is made possible by networks of polymer filaments and crosslinking molecules that connect filaments to each other and that act as motors to do mechanical work on the network. For the case of highly cross-linked filament networks, we discuss how the material properties of assemblies emerge from the forces exerted by microscopic agents. First, we introduce a phenomenological model that characterizes the forces that crosslink populations exert between filaments. Second, we derive a theory that predicts the material properties of highly crosslinked filament networks, given the crosslinks present. Third, we discuss which properties of crosslinks set the material properties and behavior of highly crosslinked cytoskeletal networks. The work presented here, will enable the better understanding of cytoskeletal mechanics and its molecular underpinnings. This theory is also a first step toward a theory of how molecular perturbations impact cytoskeletal organization, and provides a framework for designing cytoskeletal networks with desirable properties in the lab.

Commonly prescribed antidepressants, such as selective serotonin reuptake inhibitors (SSRIs) take weeks to achieve therapeutic benefits1, 2. The underlying mechanisms of why antidepressants take weeks or months to reverse depressed mood are not understood. Using a single cell sequencing approach, we analyzed gene expression changes in mice subjected to stress-induced depression and determined their temporal response to antidepressant treatment in the cerebral cortex. We discovered that both glial and neuronal cell populations elicit gene expression changes in response to stress, and that these changes are reversed upon treatment with fluoxetine (Prozac), a widely prescribed selective serotonin reuptake inhibitor (SSRI). Upon reproducing the molecular signaling events regulated by fluoxetine3 in a cortical culture system, we found that these transcriptional changes are serotonin-dependent, require reciprocal neuron-glia communication, and involve temporally-specified sequences of autoregulation and cross-regulation between FGF2 and BDNF signaling pathways. Briefly, stimulation of Fgf2 synthesis and signaling directly regulates Bdnf synthesis and secretion cell-non-autonomously requiring neuron-glia interactions, which then activates neuronal BDNF-TrkB signaling to drive longer-term neuronal adaptations4–6 leading to improved mood. Our studies highlight temporal and cell type specific mechanisms promoting the onset of the antidepressant response, that we propose could offer novel avenues for mitigating delayed onset of antidepressant therapies.