Publications

We describe an approach for many-body calculations with a finite-temperature, grand canonical ensemble formalism using auxiliary-field quantum Monte Carlo (AFQMC) with a self-consistent constraint to control the sign problem. The usual AFQMC formalism of Blankenbecler, Scalapino, and Sugar suffers from the sign problem with most physical Hamiltonians, as is well known. Building on earlier ideas to constrain the paths in auxiliary-field space [Phys. Rev. Lett. \textbf{83}, 2777 (1999)] and incorporating recent developments in zero-temperature, canonical-ensemble methods, we discuss how a self-consistent constraint can be introduced in the finite-temperature, grand-canonical-ensemble framework. This together with several other algorithmic improvements discussed here leads to a more accurate, more efficient, and numerically more stable approach for finite-temperature calculations. We carry out a systematic benchmark study in the two-dimensional repulsive Hubbard model at 1/8 doping. Temperatures as low as T=1/80 (in units of hopping) are reached. The finite-temperature method is exact at very high temperatures, and approaches the result of the zero-temperature constrained-path AFQMC as temperature is lowered. The benchmark shows that systematically accurate results are obtained for thermodynamic properties.

Extreme-precision radial velocity (EPRV) exoplanet surveys face considerable data analysis challenges in extracting maximally precise RVs from spectra. Chief among these, particularly for the upcoming generation of red-optimized spectrographs targeting M dwarfs, is the presence of telluric absorption features which are not perfectly known. Another major limitation on the achievable RV precision is the need to adopt an imperfect stellar template against which to cross-correlate or otherwise match the observations. In both cases, precision-limiting reliance on external information can be sidestepped using the data directly. Here we propose a data-driven method to simultaneously extract precise RVs and infer the underlying stellar and telluric spectra using a linear model (in the log of flux). The model employs a convex objective and convex regularization to keep the optimization of the spectral components fast. We implement this method in wobble, an open-source python package which uses TensorFlow in one of its first non-neural-network applications to astronomical data. In this work, we demonstrate the performance of wobble on archival HARPS spectra. We recover the canonical exoplanet 51 Pegasi b, detect the secular RV evolution of the M dwarf Barnard's Star, and retrieve the Rossiter-McLaughlin effect for the Hot Jupiter HD 189733b. The method additionally produces extremely high-S/N composite stellar spectra and detailed time-variable telluric spectra, which we also present here.

The dynamics and deformations of immersed flexible fibers are at the heart of important industrial and biological processes, induce peculiar mechanical and transport properties in the fluids that contain them, and are the basis for novel methods of flow control. Here we focus on the low–Reynolds number regime where advances in studying these fiber–fluid systems have been especially rapid. On the experimental side, this is due to new methods of fiber synthesis, microfluidic flow control, and microscope-based tracking measurement techniques. Likewise, there have been continuous improvements in the specialized mathematical modeling and numerical methods needed to capture the interactions of slender flexible fibers with flows, boundaries, and each other.

Current mechanisms for knowledge transfer in deep networks tend to either share the lower layers between tasks, or build upon representations trained on other tasks. However, existing work in non-deep multi-task and lifelong learning has shown success with using factorized representations of the model parameter space for transfer, permitting more flexible construction of task models. Inspired by this idea, we introduce a novel architecture for sharing latent factorized representations in convolutional neural networks (CNNs). The proposed approach, called a deconvolutional factorized CNN, uses a combination of deconvolutional factorization and tensor contraction to perform flexible transfer between tasks. Experiments on two computer vision data sets show that the DF-CNN achieves superior performance in challenging lifelong learning settings, resists catastrophic forgetting, and exhibits reverse transfer to improve previously learned tasks from subsequent experience without retraining.

We express the recently introduced real-time diagrammatic Quantum Monte Carlo, Phys. Rev. B 91, 245154 (2015), in the Larkin-Ovchinnikov basis in Keldysh space. Based on a perturbation expansion in the local interaction U, the special form of the interaction vertex allows to write diagrammatic rules in which vacuum Feynman diagrams directly vanish. This reproduces the main property of the previous algorithm, without the cost of the exponential sum over Keldysh indices. In an importance sampling procedure, this implies that only interaction times in the vicinity of the measurement time contribute. Such an algorithm can then directly address the long-time limit needed in the study of steady states in out-of-equilibrium systems. We then implement and discuss different variants of Monte Carlo algorithms in the Larkin-Ovchinnikov basis. A sign problem reappears, showing that the cancellation of vacuum diagrams has no direct impact on it.

The GW approximation is based on the neglect of vertex corrections, which appear in the exact self-energy and the exact polarizability. Here, we investigate the importance of vertex corrections in the polarizability only. We calculate the polarizability with equation-of-motion coupled-cluster theory with single and double excitations (EOM-CCSD), which rigorously includes a large class of diagrammatically-defined vertex corrections beyond the random phase approximation (RPA). As is well-known, the frequency-dependent polarizability predicted by EOM-CCSD is quite different and generally more accurate than that predicted by the RPA. We evaluate the effect of these vertex corrections on a test set of 20 atoms and molecules. When using a Hartree-Fock reference, ionization potentials predicted by the GW approximation with the RPA polarizability are typically overestimated with a mean absolute error of 0.3 eV. However, those predicted with a vertex-corrected polarizability are typically underestimated with an increased mean absolute error of 0.5 eV. This result suggests that vertex corrections in the self-energy cannot be neglected, at least for molecules. We also assess the behavior of eigenvalue self-consistency in vertex-corrected GW calculations, finding a further worsening of the predicted ionization potentials.

Observations indicate that nearly all galaxies contain supermassive black holes (SMBHs) at their centers. When galaxies merge, their component black holes form SMBH binaries (SMBHBs), which emit low-frequency gravitational waves (GWs) that can be detected by pulsar timing arrays (PTAs). We have searched the recently-released North American Nanohertz Observatory for Gravitational Waves (NANOGrav) 11-year data set for GWs from individual SMBHBs in circular orbits. As we did not find strong evidence for GWs in our data, we placed 95\% upper limits on the strength of GWs from such sources as a function of GW frequency and sky location. We placed a sky-averaged upper limit on the GW strain of $\mathith_0<7.3(3)×10^−15 at \mathitf_gw=8 nHz$. We also developed a technique to determine the significance of a particular signal in each pulsar using ``dropout' parameters as a way of identifying spurious signals in measurements from individual pulsars. We used our upper limits on the GW strain to place lower limits on the distances to individual SMBHBs. At the most-sensitive sky location, we ruled out SMBHBs emitting GWs with fgw=8 nHz within 120 Mpc for =109M⊙, and within 5.5 Gpc for =1010M⊙. We also determined that there are no SMBHBs with >1.6×109M⊙ emitting GWs in the Virgo Cluster. Finally, we estimated the number of potentially detectable sources given our current strain upper limits based on galaxies in Two Micron All-Sky Survey (2MASS) and merger rates from the Illustris cosmological simulation project. Only 34 out of 75,000 realizations of the local Universe contained a detectable source, from which we concluded it was unsurprising that we did not detect any individual sources given our current sensitivity to GWs.

Improved distance measurements to millisecond pulsars can enhance pulsar timing array (PTA) sensitivity to gravitational waves, improve tests of general relativity with binary pulsars, improve constraints on fuzzy dark matter, and more. Here we report the parallax distance measurements to six Gaia DR2 objects associated with International PTA pulsars J0437-4715, J1012+5307, J1024-0719, J1732-5049, J1910+1256, and J1843-1113. By multiplying the posteriors of the PTA distances with the \gaia distance to the companion, we improve the distance measurements, and provide a tentative detection of a previously unknown binary companion to J1843-1113. Finally, we recommend that future Gaia data releases use J0437-4715 as a calibration point, since its distance estimate in Gaia DR2 is relatively poor compared to pulsar timing measurements.

Mechanical strain is a powerful technique for tuning electronic structure and interactions in quantum materials. In a system with tetragonal symmetry, a tunable uniaxial in-plane strain can be used to probe nematic correlations in the same way that a tunable magnetic field is used to probe magnetic correlations. Here, we present a new spectroscopic scanned probe technique that provides atomic-resolution insight into the effect of anisotropic strain on the electronic structure. We use this technique to study nematic fluctuations and nematic order across the phase diagram of a prototypical iron-based superconductor. By extracting quantitatively the electronic anisotropy as function of applied strain, we show that while true long range nematic order is established at the tetragonal to orthorhombic structural transition temperature, sizable nematic fluctuations persist to high temperatures and also to the overdoped end of the superconducting dome. Remarkably, we find that uniaxial strain in the pnictides significantly enhances the amplitude of the nematic fluctuations, indicating a strong nonlinear coupling between structure and electronic nematicity.

We present a novel representation of coupled matter-photon systems that allows the application of many-body methods developed for purely fermionic systems. We do so by rewriting the original coupled light-matter problem in a higher-dimensional configuration space and then use photon-dressed orbitals as a basis to expand the thus "fermionized" coupled system. As an application we present a dressed time-dependent density-functional theory approach. The resulting dressed Kohn-Sham scheme allows for straightforward non-adiabatic approximations to the unknown exchange-correlation potential that explicitly includes correlations. We illustrate this for simple model systems placed inside a high-Q optical cavity, and show also results for observables such as the photon-field fluctuations that are hard to capture in standard matter-photon Kohn-Sham. We finally highlight that the dressed-orbital approach extends beyond the context of cavity quantum electrodynamics and can be applied to, e.g., van-der-Waals problems.